The Premier League club said both 19-year-old centre-forward Véliz and Van de Ven, 22, had agreed deals to 2029.
Véliz joins Ange Postecoglou's squad after making 62 appearances and scoring 19 goals across all competitions for Rosario since his debut in 2021.
Local media reported Spurs paid around €17 million ($18.62m) plus add-ons to the Argentine side, who completed their most expensive sale in history.
Van de Ven moved to Wolfsburg in 2021 and made 41 appearances for the Bundesliga side in all competitions while also featuring for the Netherlands Under-21 side 11 times.
At Wolfsburg, he was deployed in a back three as well as a back four as the club finished eighth.
Sky Sports television reported the deal was for a £34.5m ($43.88m) fee plus a potential £8.5 million in add-ons.
The signings were subject to international clearance and work permits. Véliz will wear the number 36 shirt and Van de Ven the number 37.
Spurs open their Premier League campaign away at Brentford on Sunday.