The 33-year-old supermodel reportedly made a decision to end her relationship with the "A Star is Born" star - with whom she has two-year-old daughter Lea De Seine - at the end of last month because the pair rarely spent any time together.
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Gaga split from her fiance Christian Carino in February, with the break-up announced shortly before her and Cooper's duet at the Oscars.
"Since Bradley and Irina have always been very private about their relationship few knew there was really for sure something going on", the source added.
He acknowledged the long hours he poured into the project at the BAFTA awards in London earlier this year, thanking Shayk for her patience through the process.
Cooper had a big year in 2018 with the release of A Star Is Born, which was nominated for eight Academy Awards and marked his directorial debut.
Find out more about Irina Shayk below. "Thank you very much".
The Yemanzhelinsk, Russia native and Limitless actor were able to maintain privacy amid the troubled times, the source told the publication.
"After awards season ended, Cooper slowed down to focus on his family, a source told PEOPLE in April 2019, sharing that the star spent "every day with his family".
But, even though sources previously told Us Weekly that Irina was "unbothered" by the performance, according to The Sun - before singing Shallow at a gig in Vegas this weekend - Gaga reportedly told the audience, 'And one more thing, be kind.
The couple have been together since 2015 and share 2-year-old daughter Lea De Seine.
Bradley Cooper and Irina Shayk were "living totally separate lives" before their split.