"I am very happy to arrive at AS Monaco," Martins told the club's official website . "I cannot wait to get back to the field with my new team-mates and do my best to help the team."
The winger had been the subject of interest from Arsenal with boss Unai Emery hoping to bring Martins to the Emirates Stadium after he was told he would only be allowed to make loan signings in January.
It was reported last week that Gunners legend Thierry Henry was set to win the battle against his former club for Martins' signature, but Monaco acted to remove their coach following a 5-1 defeat at home to Strasbourg that left them mired in the Ligue 1 relegation zone.
Former boss Leonardo Jardim has since retaken the reigns in the principality as the 2017 champions desperately strive to cling to their top-flight status.
Martins, 23, signed for Atletico from Sporting Lisbon last summer but has found playing time scarce under Diego Simeone, and had been strongly linked with a loan move away since the January transfer window opened.
Monaco owner, Russian billionaire Dmitry Rybolovlev, said: "Welcome to Gelson Martins. Gelson is a fast attacking midfielder who has shown great things in the Sporting jersey and who will be able to bring to the squad all his speed and ability."
Monaco resume their relegation battle at home to Toulouse next Saturday, when Martins will be set to make his Ligue 1 debut.