The Spaniard spent two seasons at Los Rojiblancos but made just seven first-team appearances as he was understudy to the club’s long-term number one Jan Oblak.
Adan joined Atleti in the summer of 2018 from Real Betis, where he made 165 appearances across a five-year spell, having previously been on the books of both Real Madrid and Italian club Cagliari.
As reported by Marca, the goalkeeper said his goodbyes to his teammates at Atleti ahead of joining the Portuguese club on Thursday.
A Real Madrid youth graduate, Adan became the regular shot-stopper for the club’s Castilla side and spent three seasons in the first-team squad at the Santiago Bernabeu, where he made 18 first-team appearances – seven in La Liga, seven in the Copa del Rey and four in European competition.
A former Spain Under-21 goalkeeper, Adan will now continue his career in Lisbon with Sporting CP.