Smith (pictured, right) died of a heart attack at his home in north-west London, his agent has announced.
Smith was one of the major players in British comedy in the 1980s and 90s, moving from acting to production and direction before returning to the stage in recent years.
He regularly performed alongside Griff Rhys Jones with whom he set up the independent television company, Talkback Productions.
“I still can’t believe this has happened,” Rhys Jones said.
“To everybody who ever met him, Mel was a force for life. He had a relish for it that seemed utterly inexhaustible.”
“He inspired love and utter loyalty and he gave it in return. I will look back on the days working with him as some of the funniest times that I have ever spent.”
Jones added he was “a gentleman and a scholar, a gambler and a wit. We are all in a state of shock. We have lost a very, very dear friend.”
Peter Fincham, director of television at ITV and business partner at Talkback Productions, said: “Life was always exciting around Mel. He was my friend and business partner for many years and had extraordinary natural talent with the rare gift of wearing it lightly.
“Being funny came naturally to him, so much so that he never seemed to give it a second thought. Mel and Griff were one of the great comedy acts and it’s hard to imagine that one of them is no longer with us.”
Talkback Productions went on to make a number of much-loved comedies, among them Da Ali G Show, I’m Alan Partridge and Never Mind the Buzzcocks.
Not the Nine O’Clock News producer John Lloyd said Smith had been ill for some time.
“So although it is the most awful news – I mean, it’s a tragedy, it’s a great loss, not just as an amazingly talented guy in all sorts of areas but also as a friend – I think he was not in good shape, so in some ways we try and put a good spin on it by saying it’s a relief for him.”
Stephen Fry tweeted: “Terrible news about my old friend Mel Smith, dead today from a heart attack. Mel lived a full life, but was kind, funny & wonderful to know.”