The Premier League club said both centre-forward Veliz (19) and Van de Ven, (22), had agreed deals to 2029.
Veliz joins Ange Postecoglou's squad after making 62 appearances and scoring 19 goals across all competitions for Rosario since his debut in 2021.
He also scored three goals for Argentina at this year's U-20 World Cup, where the South Americans reached the last 16.
Local media reported Spurs paid around 17 million euros ($18.62 million) 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 34.5 million pounds ($43.88 million) fee plus a potential 8.5 million in add-ons.
The signings are subject to international clearance and work permits. Veliz will wear the number 36 shirt and Van de Ven the number 37.
The signings follow those of James Maddison, Pedro Porro, Guglielmo Vicario, Manor Solomon and Ashley Philips.
Spurs open their Premier League campaign away at Brentford on Sunday.
