Financial details were not disclosed, but Spanish media reported the transfer fee for the 27-year-old Slovakia international to be worth around 30 million euros ($35.30 million).
Hancko, who was linked with a move to Saudi Arabian side Al Nassr, has made 140 appearances for Feyenoord since his 2022 move, helping them win the Eredivisie in the 2022-23 season.
"Atletico and Feyenoord have reached an agreement over the transfer of David Hancko to our club, pending the completion of the medical examination and the signing of his new contract," Atletico, who finished third behind champions Barca and Real Madrid in LaLiga, said in a statement late on Wednesday.
