Mike, who was married to former Blue Peter presenter Sarah Greene, died in hospital on Friday following complications connected to his recent heart surgery.
"I am totally stunned and heartbroken for Sarah and his family," said fellow former Breakfast Show presenter Noel Edmonds. "Mike introduced me to motor racing and I introduced him to radio.
Mike Smith died following complications connected to his major heart surgery
"He was so much more than simply a presenter," he added. "Mike was that rare individual, the consummate broadcaster in an era when professionalism, dedication and hard work were truly valued. I am typing this through the tears. I wish I had told him more forcefully and frequently how much I admired his talent and valued his support."
Simon Mayo, who also presented the Breakfast Show, tweeted his sadness at hearing the news of Mike's death and honoured his talent for radio.
"Shocked to hear of Mike Smith's death today," he posted. "Condolences to Sarah and all his family. When we joined Radio 1 in '86, he was the guy who had it all. His breakfast show was a shiny, sparkly thing, a must-listen."
Mike with his wife Sarah Greene
Mike married his long-term love Sarah in 1989 after the pair were involved in a helicopter crash which saw the radio host break his back and ankle and his girlfriend break both legs and an arm.
"The news is just devastating," said DJ Mike Reid of Mike's death. "Sarah and Mike were a wonderful couple, it is truly horrible to hear.
"I worked with Sarah for a number of years, including around the time of the crash, so I was very fond of them both," he added. "The helicopter crash was really bad but they just got on with it and married.
"Mike was a very affable guy, fantastically business-like. It's a real loss and has come as quite a shock."