The BBC confirmed his death, but did not report the cause.
The Cambridge University-educated performer was a founding member of Peter Cook's Establishment Club and is best known for his television collaborations with John Bird and Rory Bremner.
"I'm so sorry to let you know that my friend John Fortune died this morning," Bremner tweeted Tuesday, adding Fortune was a "lovely man, dear friend" and a "brilliant & fearless satirist."
Actor and scribe Stephen Fry posted a message on Twitter saying Fortune had been a "huge influence on the satire boom" while "The Walking Dead" co-star David Morrissey praised Fortune as "such a funny man."
Fortune's film credits include "Calendar Girls," "The Tailor of Panama" and "Match Point."