Fortune - who found fame on Bremner, Bird and Fortune - died peacefully after being ill for “quite a while”.
Bremner said: “He was, first and foremost a lovely man. He was very well read, a very literary man.
“He was very much a father figure and a mentor to me.”
Fortune’s agent Vivienne Clore said the veteran satire comic died with his wife, Emma, and dog, Grizelle, at his bedside.
In a statement, she said: “It is with great sadness that I write of the death of John Fortune this morning aged 74.
“He is survived by his adored wife, Emma, and three children.”
Fortune, who recently suffered a stroke, met his comedy partner John Bird in the 1960s when they were at Cambridge.
The pair became household names for The Long Johns sketches in which the double-act made witty characterisations of bumbling politicians, military figures and businessmen.
Bremner, one of the UK’s best-loved impressionists, said: “Some of the happiest and most fulfilling times of my life are working with The Two Johns as they became known.
“In a quiet way, he was one of the pillars of the anti-establishment. He was fearless as a satirist, because there was nothing that he wouldn’t do.
“He was braver than many of us in what he would do in a satirical sketch.”
Bremner said his old friend had been satirising subjects such as the banking crisis and public utilities long before they were at forefront of pubic consciousness.
“He was satirising them better and earlier than anybody else, and I think he caught the spirit of that age just brilliantly,” he said.
“To my mind he was the best combination of intelligence and humour that I have ever met.”
In 1997, Fortune won a Bafta for Best Light Entertainment Performance for his work on Rory Bremner, Who Else? alongside Bremner and Bird.
He was also nominated four times for Baftas between 1999 and 2003.
Fellow actors and comedians paid tribute to Fortune on Twitter.
Stephen Fry wrote: “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.”
John Challis, who played Boycie in Only Fools And Horses, acted alongside Fortune, tweeted: “So sad to hear that John Fortune has died.
“I played henchman to his chief villain in Cat’s Eyes and we laughed a lot. Another goodun gone.”
Friend and long-time producer on Bremner, Bird And Fortune Geoff Atkinson described him as “unique”, adding: “He was a joy to work with, an inspiration as a writer, and the funniest person you could ever meet. But it was as a friend that I valued him most.
“His partnership with John Bird seemed effortless on air yet every week they’d sit with a blank sheet of paper and 10 minutes to fill in five days’ time - that they filled it so brilliantly week after week never failed to amaze me.
“He steered and shaped the shows we made (nearly 150) and it was his soul that sat at the heart of what we did.
“Honest, kind, caring, over 20 years, I benefited so much from his quiet wise words as a friend, and an inspiration. It’s horrible to know we’ll never hear George Parr’s voice again.”