The 24-year-old, who played for Croatia at Euro 2016, was under contract with Sassuolo until June 2019 and arrives in La Liga after playing for three seasons in Serie A.
"Sime Vrsaljko is an Atletico Madrid player. The Croatian international has signed a five-year contract until 2021 after the club reached an agreement with Sassuolo," said a statement from the Spanish club.
Atletico did not give any financial details but Spanish media estimated the transfer fee at 16 million euros (13.60 million pounds).
Vrsaljko, who started out at Dinamo Zagreb and played 58 times for Sassuolo in the last two campaigns following a season with Genoa, was thrilled to be joining Diego Simeone's side.
"To play at Atletico is a great challenge for me, I'm delighted," he told the club's official website (en.clubatleticodemadrid.com).
Atletico sporting director Jose Luis Perez Caminero reckoned Vrsaljko was a great addition to his club.
"He is a player with an enormous projection," Caminero said. "He fits perfectly with our idea of bringing in football players that increase the competitiveness and the level of the group."
(Repoerting by Adriana Garcia; Editing by Ken Ferris)
