The Premier League runners-up agreed a fee for Rice worth £100 million ($131m) plus £5m ($6.5m) in add-ons, sources told ESPN. The amount easily eclipses Arsenal's previous record fee -- the £72m paid to sign Nicolas Pepe from Lille in 2019.
When all is said and done, Rice, 24, may also become the most expensive British player in Premier League history, eclipsing the £100m Manchester City paid to sign Jack Grealish from Aston Villa two years ago.
"It's been a bit overwhelming because of my relationship with West Ham. [With] the love and support I have for them, it's been really hard to walk away," Rice said.
"In football, amazing opportunities arise. Big clubs, like Arsenal, have come for me and it's really hard to turn down. You only ever get one career and I really believe in what Mikel is building here and the squad he's building. I'm really looking forward to the future with Arsenal."
Rice's arrival follows the signing of Germany international Kai Havertz from Chelsea for a fee worth up to £67.5m as Arsenal continue to add firepower to the squad that mounted an unexpected Premier League title challenge last season.
Arsenal eventually fell short to title eventual treble winners City but came out on top in the race to sign Rice.
City had an earlier offer of £80m plus £10m in add-ons rejected, sources told ESPN, but believed Arsenal's bid exceeded their valuation.
He will join Arsenal on their preseason tour of the United States, with the Community Shield against City on Aug. 6 his first chance to make his competitive debut. Arsenal begin their 2023-24 Premier League campaign by hosting Nottingham Forest on Aug. 12.
West Ham long expected Rice, who had one year left on his contract plus the option of another year, to leave this summer after guiding the club to the Europa Conference League title last month. The club confirmed his exit earlier on Saturday.
"Everyone at West Ham United should be very proud of the part we have played in his journey from the Academy of Football at Chadwell Heath to becoming the most valuable young player in English football," West Ham joint chairman David Sullivan said in a statement.
Arsenal had their opening two offers for Rice rejected, sources told ESPN, including a bid last month of £75m plus £15m in add-ons.
Manchester United had also been linked to Rice, but they were not able to match West Ham's valuation.
Rice had spent his entire senior career at West Ham, making his first-team debut in 2017 and being named the club captain ahead of the 2022-23 season. After making his debut in 2019, Rice has gone on to make 43 appearances for England.
"I knew from the very first moment I walked into Chadwell Heath [training ground] that I had found another place I could call home," Rice said in an open letter to West Ham fans.
"I look back now and realise how crucial my time at Chadwell Heath was in shaping me, as a footballer and as a man. ... I found the perfect place to build my confidence, enabling my focus, determination and ambition to flourish.
"I want you to know how tough a decision it has been for me to leave an environment that I have loved and cherished so much. Ultimately, though, it has only ever been about my ambition to play at the very highest level of the game."