The 24-year-old Portugal international, who was on loan at Monaco last season, has arrived for an undisclosed fee.
Cape Verde-born Martins played only eight LaLiga matches for Atlético following his move from Sporting Lisbon in 2018.
However, he had a prosperous loan spell at Monaco, playing 16 Ligue 1 games and scoring four goals as they secured their top-flight status.
A statement on the club’s Twitter account read: “AS Monaco is thrilled to announce the signing of @GelsonMartins.
“Originally on loan from Atlético Madrid, the attacking midfielder has put pen to paper on a five-year permanent deal.”