His agent, Vivienne Clore, said he had died peacefully, with his wife Emma at his bedside.
Rory Bremner tweeted: "I'm so sorry to let you know my friend John Fortune died this morning. Lovely man, dear friend, brilliant & fearless satirist."
He went on to describe Mr Fortune as "the most lovely man" who "had the most beautiful brain of any man I've ever known".
"In some ways Bird and Fortune were the pillars of the anti-establishment," he told the BBC. "Their timing was so superb and they had the ability to dissect a subject like a scalpel."
Broadcaster Stephen Fry tweeted: "Oh how sad John Fortune has died. He was in the first play I was ever in, 40 Years On. Huge influence on the satire boom."
Ms Clore said: "It is with great sadness that I write of the death of John Fortune aged 74. He died peacefully with his wife, Emma and dog Grizelle, at his bedside."
He is survived by his wife and three children.
Mr Fortune was best known for his sketches alongside John Bird. The pair became well known for The Long John's skits in which the double-act portrayed politicians, military figures and businessmen.
In 1997 he won a Bafta for Best Light Entertainment Performance for his work on Rory Bremner, Who Else? alongside Bremner and Bird.
A former member of the Cambridge Footlights, Mr Fortune also appeared in films including Calendar Girls, The Tailor of Panama and Woody Allen's Match Point.