The arrival of the 30-year-old may pave the way for the departure of fellow shot-stopper Thibaut Courtois, who is widely expected to return to parent club Chelsea.
Courtois has spent the last three seasons on loan at Atletico.
Moya – formerly of Mallorca and Valencia – spent three seasons at Getafe and made 26 appearances for the club last term.
A statement on Atletico's website confirmed the deal and read: "Atletico de Madrid and Getafe have reached an agreement for the transfer of Miguel Angel Moya.
"(It is) pending the goalkeeper undergoing the corresponding medical examination and signing his contract with our club.
"The goalkeeper (will play at Atletico) for the next three seasons."
Atletico claimed a historic Liga win last term, ending an 18-year drought to be crowned champions of Spain.
And they were close to sealing a stunning double when they led city rivals Real Madrid 1-0 in the UEFA Champions League final.
Sergio Ramos' injury-time header forced extra-time, though, and Real went on to win 4-1.
