Diego Simeone's side, currently serving the final window of their FIFA signing ban, will register Vitolo from January 1, before which he will play for fellow La Liga side Las Palmas.
The complex transfer comes two days after Sevilla president Jose Castro claimed the 27-year-old had in fact signed a new five-year deal with his club.
"Atletico de Madrid has reached an agreement with Victor Machin Perez, Vitolo, for the next five years after the player rescinded his contract with Sevilla," read Atletico's statement on Wednesday.
"Due to FIFA's sanction that forbids the club from registering football players during the current summer market, the player will play the first half of the season with Las Palmas and will join our team starting on January 1, 2018.
"The Spain international has signed with our club until the June 30, 2022."