The 28-year-old, who also featured in last month's World Cup final when Argentina lost their crown to Spain, cost Roma a reported 17 million euros ($20 million).
The 65-times capped defender has also won two Copa Americas in 2021 and 2024 and made 249 appearances and scored 19 goals in all competitions in Europe while playing for Udinese and Atletico Madrid, Roma said.
Molina could make his debut when Roma, who are back in the Champions League after a seven year hiatus, play Fiorentina in their Serie A opener on August 24.