Atletico said De Paul joined the club on a five-year contract. He had been with Italian club Udinese since 2016.
De Paul started for Argentina in the Copa America final against Brazil on Saturday, when the Argentines won 1-0.
"I'll be joining the Spanish league champion and I know that it is a big responsibility,'' he said. "It's a big step in my career.''
De Paul played two season with Spanish club Valencia before joining Udinese. He will be at Atletico under Argentine coach Diego Simeone.
Atletico are fresh off winning the La Liga title, the team's 11th in club history and second under Simeone, who recently extended his deal to manage Atleti through the 2024 season.
"I'll enjoy being under his command because I grew up watching him play with Argentina's national team,'' De Paul said.
Financial details of the transfer between Atletico and Udinese were not immediately released by the clubs.