The Spanish champions, who have yet to reach an agreement with Chelsea over the future of Belgium No.1 Thibaut Courtois, have reportedly paid €3 million [£2.4m] for the 30-year-old
The 30-year-old made 26 appearances for Cosmin Contra's side last season before a knee injury in March brought his campaign to an early end.
Atletico have now moved to secure a deal believed to total €3 million [£2.4m] for the former Spain youth international, who will join the Vicente Calderon outfit until 2017, pending a successful medical.
The news, confirmed via the Spanish champions' official website, raises further question marks over the future of Belgium No.1 Thibaut Courtois.
The 22-year-old, who has spent the last three seasons on loan from Chelsea, has been embroiled in transfer tug-of-war between the Blues and Diego Simeone's side.
Courtois himself claimed earlier in the Spring that he felt "no connection" with Chelsea, having never featured for the club, while Atletico chief Miguel Angel Gil Marin said the Belgian was eager to stay in the Spanish capital on a permanent basis.
However, Courtois hinted last week that a return to London could be better in the long term, and Moya's arrival will do little to dispel doubts over whether Atletico can reach a deal to keep him at the club.