When asked if he will remain faithful to the woman he already calls his wife, though they aren't expected to marry until October, he replied: "You have to be. That's one of the things about this institution of marriage."
"My wife recently explained to me, 'You must be faithful' and I don't have a problem with that. I'm really, really in love," the 34-year-old told The Sun.
The pair were in Los Angeles on Tuesday night for the premiere of Russell's new movie, Get Him To The Greek.
With Russell dressed head to toe in white and Katy in a striking silver gown, they mingled with co-stars including Superbad actor Jonah Hill and Sean "P Diddy" Combs.
In the movie Russell reprises the role of rock star Aldous Snow, who he played in 2008 comedy Forgetting Sarah Marshall.
The plot sees record company intern Aaron - played by Jonah - charged with escorting Aldous from London to a comeback gig at LA's famous Greek Theatre.
The film also features cameos from a variety of other big names in music, including Christina Aguilera and Pink, while P Diddy plays a record exec.
Other loved-up guests at the movie launch, which was held at the theatre of the comedy's title, included High School Musical couple Zac Efron and Vanessa Hudgens.
Both dressed in grey tones, the pair cuddled up close on the red carpet.
Get Him To The Greek is set to be released in the UK on June 25.