He passed away on Wednesday (28Nov12) at the University of Southern California's Norris Comprehensive Cancer Center.
Announcing the news in a post on the star's blog, RadiateDon.com, his wife Kate writes, "My sweet husband, the love of my life, passed away early Wednesday morning. We had been married 29 years, 6 months, and 7 days, and I'm left with a gaping hole in my heart. He was the strongest, most generous and most honest person I've ever known. Oh yeah, and he was funny too."
A memorial service for his fans, friends and family is set to take place in Los Angeles on Monday (03Dec12).
Rhymer is perhaps best known for penning animated family movies Rio and Surf's Up, as well as comedies Big Momma's House, Deck the Halls, The Santa Clause 2, and Agent Cody Banks 2: Destination London.
His list of credits also includes writing for hit U.S. TV shows The Hogan Family and Evening Shade.
The scribe's last project, a sequel to Rio, which features the voices of Anne Hathaway and Jesse Eisenberg, will be released in early 2014.