The 21-year-old defender joins the Saints on a four-year contract after an impressive debut season in La Liga with Real Valladolid.
Southampton manager Ralph Hasenhuttl told the club's official website the following:
"This is an important signing for us. Mohammed is a player who fits our profile well. He is young and has a great amount of potential, but he is also someone who has the qualities to come in and help the team as soon as he is up to speed with our way of playing.
Odegaard, who was signed in 2015 at age 16, has played just twice for Real Madrid's first team to date, having spent time on loan at Heerenveen, Vitesse and Real Sociedad.
17.36 BST: Austin FC, who will begin play during the 2021 MLS season, are set to sign their second ever player in Paraguayan winger Cecilio Dominguez.
The 26-year-old arrives from Argentine side Independiente, and is the second Paraguayan attacker to join the expansion side, following the signing of forward Rodney Redes last month. Dominguez, who has also spent time in Mexico with America, will join Austin for around a $4 million fee, according to ESPN Argentina.
17.00 BST: Chelsea have some transfer plans but they're already ahead of the rest.
16.07 BST: La Gazzetta dello Sport reports that Roma could swap Amadou Diawara for Arsenal midfielder Lucas Torreira.
Torreira, 24, admitted earlier this month to Uruguayan radio station Sport 890 that "it will be for the best" if he leaves the Gunners, with AC Milan also keen.
Diawara made 30 appearances as Roma finished fifth in Serie A but the 23-year-old has been linked with a move away and Tottenham, Leicester and Leeds are monitoring him.
15.31 BST: Watford have been relegated from the Premier League but that won't stop them demanding top dollar for their best players.
The Evening Standard reports that Ismaila Sarr is of interest to Liverpool but the club want at least a club-record fee of over £40m for him, having spent £30m to sign Sarr from Rennes last summer.
Sarr, 22, has been tracked by Crystal Palace and Wolves but idolises fellow Senegal international Sadio Mane, so one assumes he would prefer a move to Anfield.
14.40 BST: Schalke's 21-year-old United States international Weston McKennie is attracting plenty of attention this window.
14.05 BST: Arsenal are really keen to land Sporting CP starlet Joelson Fernandes.
A Bola reports that the Gunners made a €20m bid, which was rejected, and have now returned with €32m. That was also rejected, with the Portuguese side holding out for his release clause of €45m.
It may help that the player's agent is Kia Joorabchian, who has a good relationship with the London club, while Barcelona and Juventus are reported to be showing an interest in the 17-year-old dubbed 'the new Cristiano Ronaldo'.
13.41 BST: Tahith Chong and James Garner are set to head the list of Manchester United loan exits this summer, sources have told ESPN's Rob Dawson.
The pair are training with Ole Gunnar Solskjaer's senior squad in Germany during the Europa League mini tournament but will be granted temporary moves ahead of next season.
Dylan Levitt, Matej Kovar, Di'Shon Bernard and Ethan Laird are among the other United youngsters being considered for loan moves but defender Teden Mengi is set to remain at Old Trafford after making his first-team debut in the 2-1 win over LASK Linz.
Werder Breman are leading the chase for Chong, who has made 16 first team appearances since arriving from Feyenoord in 2016.
The 20-year-old, capped six times by Netherlands Under-21s, signed a new deal in March that could keep him at the club until 2023.
Garner, who has played for the senior team seven times, has been earmarked for a move to the Championship or League One.
13.02 BST: Update from this morning: Chelsea are willing to sell Tiemoue Bakayoko to AC Milan but are aiming to recoup almost all of the £40m they spent to sign the midfielder from Monaco in 2017, sources have told ESPN's James Olley.
Milan are keen on bringing Bakayoko back to the San Siro (where he spent time on loan) and although Chelsea are willing to do business, they would prefer a straight sale or a loan with an obligation to buy rather than an option.
One report in Italy suggests Milan are prepared to offer a £2.6m loan fee with an option to buy fixed at £31m. Those figures bring an overall deal close to Chelsea's valuation but further talks are expected.
12.46 BST: Manchester City midfielder David Silva looks set to continue his career in Italy.
12.10 BST: Barcelona winger Ansu Fati's name is back on Manchester United's radar, according to a report in Diario Sport, as the English side seek alternatives to Borussia Dortmund's Jadon Sancho.
ESPN reported on Tuesday that Barcelona's Ousmane Dembele is one of United's backup options, along with Bayern's Kingsley Coman and Juve's Douglas Costa, with Sport claiming Fati is also on that list.
United were linked with the teenager earlier in the year but their interest was immediately knocked back by Barca. The 17-year-old signed a new deal last year with a €170m release clause, which will rise to €400m once he's officially promoted to the first team.
Therefore, with Barca not wanting to sell, any deal for Fati would likely be worth more than one for Sancho, making it an avenue United are unlikely to go down.
11.49 BST: Diario Sport suggests Barcelona are interested in signing Valencia defender Jose Luis Gaya as they look to increase the competition for Jordi Alba.
Sources have told ESPN's Sam Marsden and Moises Llorens that Barca's are prioritising moves for Eric Garcia and Lautaro Martinez in the transfer window but they could look to move for another left-back if they sell Junior Firpo.
Gaya, 25, has a €50m release clause but Barca could look to take advantage of the institutional mess at Valencia, who have just sold midfielders Dani Parejo and Francis Coquelin to Villarreal for around €10m.
Sport reports that Watford's Pervis Estupinan, who impressed on loan at La Liga side Osasuna this season, is another option Barca are considering.
11.20 BST: Barcelona's Ousmane Dembele or Juventus' Douglas Costa...?
10.59 BST: Manchester United's pursuit of Dortmund winger Jadon Sancho is turning into a real saga, but they could have another option.
The Manchester Evening News thinks that the club could hijack Chelsea's €80m deal for Kai Havertz.
The two are completely different types of player, so it would be interesting to see what the United logic is other than 'we want to make a statement signing' but Havertz would be a quality addition to any team.
10.25 BST: Villarreal have announced the signing of Valencia midfield duo Francis Coquelin and Dani Parejo.
The La Liga club have already revealed the arrival of the ex-Arsenal midfielder Coquelin, while Spain international Parejo has been spotted arriving at their training ground.
The pair are available at a bargain price, with Coquelin moving for a reported €8m, and Parejo for no initial fee, with various sums payable later based on performance.
Valencia are in a difficult financial situation and, needing to cut their wage bill, have put the majority of their squad on the market as they look to balance the books for next season.
Coquelin and Parejo will form a new-look midfield for Villarreal coach Unai Emery alongside loan signing Takefusa Kubo, who joined from Real Madrid earlier this week.
10.03 BST: Leicester striker Kelechi Iheanacho is being linked with a loan move to Fenerbahce.
Turkish website Fotospor says that the 23-year-old will replace Vedat Muriqi, who is on the way to Lazio, and they are willing to pay €12m to loan him for two years.
09.32 BST: Will Bayern Munich midfielder Thiago end up at Liverpool?
08.51 BST: Chelsea are looking to raise funds and unwanted midfielder Tiemoue Bakayoko is top of the list.
Bakayoko, 25, has spent two years out on loan after signing from Monaco for £40m in 2017. Now the Blues want to move him on and will reportedly accept offers in the region of £20m for the Frenchman.
The Sun reports that AC Milan are keen but are only willing to pay £13.5m, which falls short of the valuation.
08.23 BST: Martin Odegaard is expected to play for Real Madrid next season, multiple sources have told ESPN's Alex Kirkland and Rodrigo Faez, after the club told Real Sociedad they want to end the 21-year-old's loan spell early.
The move is a shock for the Basque club, who had been convinced that the midfielder would spend a second season in San Sebastian.
08.00 BST: Manchester United will continue to pursue a deal for Borussia Dortmund winger Jadon Sancho but have sounded out Barcelona's Ousmane Dembele as a possible alternative, sources have told ESPN's James Olley.
Dortmund sporting director Michael Zorc cast doubt over the 20-year-old's long-anticipated move to Old Trafford when he said the club "plan on having Sancho in our team this season," adding that the decision on his future was "final."
Sources said that United have held informal talks over a move for Dembele, who has two years left on his contract. The 23-year-old has not played a competitive match since November and underwent surgery on his hamstring in February.
PAPER TALK (by Liam Wheeler)
Juventus willing to offer three players in deal for Lacazette
Juventus will reportedly make three players available to Arsenal as the Old Lady step up their pursuit of forward Alexandre Lacazette.
The Athletic had revealed the North London club might be forced to let the France striker leave to save money, with Juventus identified as potential suitors as new boss Andrea Pirlo looks to refine his squad ahead of the new campaign.
And now the Mirror adds that Pirlo is willing to offer the Gunners their pick of Gonzalo Higuain, Douglas Costa or Cristian Romero in a bid to entice the club to sanction a deal.
Winger Costa was reported as being a "non-starter" based on his wages and a lack of interest in linking up with Arteta's side, but Tuttomercatoweb says that's not the case, stating that the Gunners would be willing to agree to a swap deal.
Silva will join Lazio after UCL campaign
Rumours that Manchester City legend David Silva will head to Serie A at the end of the season have been building momentum over the past few days, with Lazio suspected to be the Spaniard's next destination.
According to a report in the Guardian, that deal is now pretty much done with Silva, 34, expected to sign a three-year-deal with the Biancocelesti when he finally leaves Manchester City after their Champions League campaign ends.
That would make Silva the ripe old age of 37 upon the end of his next contract, but the midfielder says he believes he has five more years in him at the highest level.
However, before that, there is still the small matter of a Champions League campaign to complete, with Silva determined to go out on the highest of highs ahead of a quarterfinal matchup with Lyon.
Meanwhile, Lazio are said to be close to extending the contract of star man Ciro Immobile and are in advanced talks to sign Vedat Muriqi from Fenerbahce in a £14m deal.
Tap-ins
- Southampton are finally expected to announce the signing of Real Valladolid defender Mohammed Salisu in the coming days, the Daily Mail reports. Saints paid the 21-year-old's £10.9m release clause last week, but the player was forced to spend 14 days in isolation prior to linking up with his new club.
- Newcastle's £300m takeover may be on hold, but the club are at least said to be close to their first signing of the summer. The Northern Echo reports that talks with midfielder Jeff Hendrick are at an advanced stage following the expiration of the 28-year-old's Burnley contract.
- This one might leave Chelsea fans angry. According to Sky Sports, West Ham have denied reports of a £50m bid from the Blues for Declan Rice and would "laugh off" any such offer. The Hammers are determined to keep hold of their star man, who is under contract until 2024, while West Ham also have an option of an extra year.
- In other news, the same outlet reports that Bayern Munich's Thiago Alcantara would "love to play for Jurgen Klopp." In fairness, who wouldn't? Sadly for Thiago, though, Liverpool aren't currently on the lookout for a midfielder, but the 29-year-old will be considered should that change. Thiago has already told his current employers that he will seek a new challenge when his contract expires next summer.
