The pair packed on the PDA at the event, stopping to kiss for the cameras on several swoon-worthy occasions.
Kate and Daniel were first spotted together in Los Angeles in March earlier this year, but hadn't confirmed the romance until now.
Speaking at the premiere to Entertainment Tonight, stepdad Kurt Russell said: “He’s a nice guy, Danny. Yeah, I like him. I always approve. Kate brings good guys."
Goldie also gushed about Kate’s new man, saying “He’s a great guy. Yeah, he’s very special actually.”
Kate has certainly favoured musicians over the years, first marrying Chris Robinson of the Black Crowes in 2000 and welcoming son Ryder Russell Robinson, before separating in 2007. She later became engaged to Matt Bellamy in 2011, and welcomed son Bingham Hawn Bellamy before splitting in 2014.
Congratulations to the happy couple!