US reports earlier this week revealed the pair's relationship was "hanging on by a thread".
Cooper was linked to Lady Gaga, 33, earlier this year after their electrifying performance at the Academy Awards stunned the world.
Oscar-nominated Cooper performed a sexually-charged duet of Lady Gaga's song Shallow from their hit movie A Star Is Born.
The pair's onstage chemistry at the Oscars sent social media into a meltdown.
Lady Gaga was forced to defend the performance, saying it was all an act.
"(Shallow) is a love song, A Star Is Born is a love story," Gaga said.
"It was so important to both of us that we were connected the entire time … When you're singing love songs, that's what you want people to feel."
Cooper and Shayk's break up comes as Lady Gaga also recnetly split from her fiance Christian Carino.
Gaga and Carino revealed in February they had called off their engagement after two years of dating.
Over the weekend, she told fans at a performance of her song Someone to Watch Over Me at her residency in Las Vegas she would be singing her song without a ring on her finger.