"We have been watching him over the last year and we saw him in the Europa League," Atletico manager Diego Simeone told reporters in Singapore on Wednesday.
"He will bring us added strength on the right hand side of the attack and can even play in an attacking trio."
Martins rescinded his contract with Sporting last month, one of nine players to quit the Lisbon club after an attack in May on a training camp by fans in which Dutch forward Bas Dost was injured and the dressing room was vandalised.
The incidents came at the end of a tumultuous campaign for Sporting who finished third in the Primeira Liga and reached the Europa League quarter-finals where they lost 2-1 on aggregate to eventual winners Atletico. Martins played in both legs.
"Our club has reached an agreement with Gelson Martins, making him a new Atletico player," said a statement from last season's La Liga runners-up. "The Portuguese attacker, who arrives as a free agent, has signed for six seasons."
Simeone added: "We are happy with his arrival and we will try to get him involved as soon as possible to see where he can position himself within the team."
The 23-year-old has been capped 19 times for Portugal and was part of their squad for the 2018 World Cup in Russia, appearing as a substitute in the 1-0 win over Morocco.
Martins is Atletico's fifth close-season signing after Thomas Lemar from AS Monaco, Rodri (Villarreal), Jonny Castro (Celta Vigo) and Antonio Adan (Real Betis).
(Reporting by Richard Martin; Additional reporting by John O'Brien in Singapore; Editing by Christian Radnedge and Ken Ferris)
