The 61-year-old musician was piloting a small aircraft when it crashed into a remote area near north of Santa Barbara on June 22.
His death was later confirmed by his assistant Sylvia Patrycja on Facebook.
"We have lost an amazing person with a huge heart and unbelievable talent. He died doing what he loved. Thank you for all your support and love and see you down the road," Patrycja wrote.
Horner won the Oscar for best original score for his work on James Cameron's "Titanic" and followed it with original song win for Celin Dion-sung "My Heart Will Go On" in the film. He shared the award with songwriter Will Jennings on the popular number.
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The "Star Trek" composer, one of the busiest musicians in Hollywood, gave music for two other best picture winners: Mel Gibson-starrer "Braveheart" and "A Beautiful Mind". His other nominations were for "An American Tail", "Field of Dreams", "Apollo 13" and "House of Sand and Fog".
Horner's work will be seen in upcoming films "Southpaw"; "Wolf Totem" and "The 33".
Dion was one of the first celebrities to pay tribute to Horner.
"Rene and I are deeply saddened by the tragic death of James Horner. He will always remain a great composer in our hearts. James played an important part in my career. We will miss him. We offer his family and friends our deepest sympathy," Dion said.
"I count James Horner among the very best film composers of our generation. His work is stirring, emotionally powerful and broadly evocative.
"Although we only met on a few occasions, I will always cherish the memory of him and his wonderful work," composer Alan Menken said.
Marco Beltrami, composer on "The Hurt Locker", "World War Z" and "3:10 to Yuma" said, "James Horner was one of the great film composer legends. I can't help feeling that his passing marks the end of an era."
"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," tweeted director James Wann.
Actor Russel Crowe also paid tribute to "A Beautiful Mind" composer. "My sincere condolences to the family, loved ones and friends of James Horner. #abeautifulmind."
Actor Seth MacFarlane posted, "Incredibly saddened to hear about the loss of James Horner. I grew up loving his work. He leaves behind a spectacular musical legacy."
"Listening to the #Braveheart score on the radio right now in honor of #JamesHorner. Reminded of what a huge loss his passing is. RIP," tweeted actor Josh Gad.