The `California Gurls` singer - who got engaged to the British comedian in December after a whirlwind romance - is planning to serenade Russell with the romantic tune when they get married later this year.
A source explained: "Katy has written a lovesong for Russell. She`s planning to sing it to him right after they exchange vows.
"She can`t wait to see the look on his face. It`s going to be the most emotional moment of her life. Katy`s fallen head-over-heels for Russell and isn`t afraid to show everyone her inner feelings. She thinks that the best way she can express herself is with romantic lyrics."
Katy, 25, recently revealed she and 35-year-old Russell keep making up stories about their impending nuptials so people will be surprised when the big day finally arrives.
She said: "Russell makes up these really crazy stories about me and our wedding. I make up stories, too - I said he was a `groomzilla`. He said I farted a lot, but I`ve never farted in front of him - honestly!
"I hear these crazy stories - we are going to get married in latex, underwear, in Spandex, in Japan, in India, in Thailand. But I think all this craziness about my marriage is really funny.