The aircraft came down in the Los Padres National Forest, north of Los Angeles, triggering a fire that charred more than an acre of brush, local fire authorities said.
Hollywood stars such as Russell Crowe and Kirstie Alley paid tribute to Mr Horner on Twitter after The Hollywood Reporter and Variety magazine reported he had died in his private plane.
Director Ron Howard, who worked with him in A Beautiful Mind, wrote:
Brilliant Composer James Horner, friend & collaborator on 7 movies has tragically died in a plane crash. My heart aches for his loved ones.
— Ron Howard (@RealRonHoward) June 23, 2015Here's what other celebrities tweeted:
My sincere condolences to the family, loved ones and friends of James Horner. #abeautifulmind
— Russell Crowe (@russellcrowe) June 23, 2015I"m so sad to hear about James Horner..He scored the first movie I did..Star Trek 2...great composer..great person...huge loss
— Kirstie Alley (@kirstiealley) June 23, 2015RIP JAMES Horner
— Kirstie Alley (@kirstiealley) June 23, 2015Incredibly saddened to hear about the loss of James Horner. I grew up loving his work. He leaves behind a spectacular musical legacy.
— Seth MacFarlane (@SethMacFarlane) June 23, 2015There is nothing that shaped my movie-going experience more than the musical genius of James Horner. He will live on through the ages.
— Rob Lowe (@RobLowe) June 23, 2015This is such heart-wrenching news. James Horner's music guided me thru my teenage years. My dreams and daydreams were set to his scores.
— James Wan (@creepypuppet) June 23, 2015"If we hold on together, I know our dreams will never die. Dreams see us through to forever." RIP James Horner. You'll be sadly missed.
— James Wan (@creepypuppet) June 23, 2015We lost a MASTER today. RIP James Horner. Your music will live forever... https://t.co/qi4n0hiX0d
— Debra Messing (@DebraMessing) June 23, 2015Mr Horner, 61, won two Academy Awards for his work on Titanic, one for the score and one shared with lyricist Will Jennings for best original song - My Heart Will Go On, performed by Celine Dion.
Mr Horner also composed the music for Aliens, The Karate Kid, Braveheart and a string of other major films. His scores for Avatar, A Beautiful Mind and House of Sand and Fog earned him Oscar nominations.
His attorney Jay Cooper earlier told Reuters he had not heard from Mr Horner since the crash, but could not confirm whether he was on board at the time. "He's an experienced pilot, but I know nothing else," Mr Cooper had said.
The Ventura County Fire Department said the plane crashed at 9:30 a.m. (1630 GMT Sunday) and there were no survivors. The cause of the crash was not immediately known.
