Gelbart, who was diagnosed with cancer in June, died at his home in Beverly Hills, said his wife, Pat.
Jack Lemmon once described the genial, quick-witted Gelbart as "one of the greatest writers of comedy to have graced the arts in this century."
"Larry Gelbart was among the very best comedy writers ever produced in America," said Mel Brooks, whose friendship with Gelbart dated to when they both wrote for Sid Caesar's comedy-variety show "Caesar's Hour" in the 1950s. Gelbart "had class, he had wit, he had style and grace. He was a marvelous writer who could do more with words than anybody I ever met," Brooks said.
In a statement Friday, Woody Allen called Gelbart "the best comedy writer that I ever knew and one of the best guys."
Said Carl Reiner, who had also known Gelbart since the "Caesar's Hour" days when Reiner was a cast member: "The main thing about Larry, he was a comedy prodigy who developed into a national treasure. The man was one of the most gifted satirists who ever lived."
For many, Gelbart is best remembered for his work on "MASH," the long-running series whose blend of laughter and tragedy made TV history.
Set in the 4077th Mobile Army Surgical Hospital during the Korean War, TV's "MASH" grew out of director Robert Altman's hit 1970 movie written by Ring Lardner Jr., which was based on the 1968 novel by Richard Hooker (the pen name of Dr. Richard Hornberger, who had been a military surgeon in Korea).
Gelbart and his family were living in London, and he was producing the British TV show "The Marty Feldman Comedy Machine" in 1971 when producer-director Gene Reynolds called him about writing a pilot script for a TV series based on "MASH."
In writing the pilot, Gelbart recalled in his 1998 memoir "Laughing Matters," he knew that it "was going to have to be a whole lot more than funny. Funny was easy. How not to trivialize human suffering by trying to be comic about it, that was the challenge."
"MASH" debuted on CBS in 1972, with Gelbart serving as executive script consultant. He and Reynolds were both executive producers of the show -- and shared Emmys -- when it won the award for outstanding comedy series in 1974.
Gelbart's influence on "MASH," Reynolds told the New York Times in 1989, was "seminal, basic and enormous."
"Larry not only had the wit and the jokes," Reynolds said, "he had a point of view. He not only had the ribald spirit, he had the sensibility to the premise -- the wastefulness of war."
As for the regulation-breaking surgeon Hawkeye Pierce -- the lead character played by Alan Alda -- Gelbart told the New York Times, "I didn't have to think of why he was saying what he said. He was saying what I felt. I mean, he is an idealized me."
Hawkeye, he said, "is capable -- that is, at work, at what he does. He's an idealist. He's a romantic. Somebody who cares about himself and other people. He's often frustrated by whatever particular system he finds himself fighting against."
"MASH" ran for 11 years. But Gelbart's involvement ended in 1976 after four years and 97 episodes. As he later told The Times, "After four years, I had given it my best, my worst and everything in between."
In a statement Friday, Alda said: "Larry's genius for writing changed my life because I got to speak his lines -- lines that were so good they'll be with us for a long, long time; but his other genius -- his immense talent for being good company -- is a light that's gone out and we're all sitting here in the dark."
Gelbart's more than 60-year career began in radio during World War II when he was a 16-year-old student at Fairfax High School in Los Angeles.
He wrote for "Duffy's Tavern" and radio shows starring Eddie Cantor, Joan Davis, Jack Paar, Jack Carson and Bob Hope, with whom he traveled overseas when Hope entertained the troops.