Accepting the trophy for Best Original Music at the London ceremony on Sunday, Cooper, 44, gushed (via Us Weekly), "I got to fulfill a dream I never thought would happen. I share this with Lady Gaga tonight, the music was the heartbeat of this film."
"I also need to thank Irina for putting up with me while I was trying to make music in our basement for a year," he added.
Shayk, 33, reportedly gave her man a standing ovation.
Cooper and Shayk have been dating since 2015 and share daughter Lea De Seine Shayk Cooper.
Gaga, meanwhile, was cleaning up at the Grammys on Sunday for "A Star Is Born" and performing "Shallow," but shared her teary gratitude for the BAFTAs victory.
"I can’t believe we just won Best Original Music @BAFTA ‘s," she tweeted. "I wish so much I was there but am at the Grammy’s to show them our love as well. We made a film about music. This means the world to me. Thank u to all our fans we love u so much, we wouldn’t be here without u #BAFTAs."
Gaga and Cooper won Best Song Written for Visual Media and Best Pop Duo/Group for "Shallow." Gaga thanked the "A Star Is Born" director profusely during her acceptance speech, telling the crowd, "I wish Bradley was here right now. I know he wants to be here. Bradley, I loved singing this song with you."