The 59-year-old, who Diana, Princess of Wales famously referred to as her “favourite DJ”, passed away on Friday.
Smith, who had been married to former Blue Peter presenter Sarah Greene for 25 years, spent six years at Radio 1, hosting the breakfast show for two.
In a statement released by Smith’s company Flying TV, Greene asked that her family and friends be allowed to mourn their loss in peace, as well as thanking staff who had treated him in hospital.
Speaking last night, fellow Radio 1 alumnus Mike Read said the news of his former colleague’s death was “devastating” and had come as “quite a shock”.
Smith started his career in broadcasting on hospital radio before moving to Capital Radio and then joining BBC Radio 1 in 1982.
In 1983, Smith had the weekday lunchtime show before taking over the breakfast show from Mike Read, hosting it for two years before quitting the channel in 1988.
During his two-year stint in the job, Diana, Princess of Wales, stated that he was her favourite DJ. He was also a presenter on Top Of The Pops and hosted the BBC’s coverage of Live Aid in 1985.
In 1988, shortly before becoming engaged to Greene, the couple were seriously injured in a helicopter crash in Gloucestershire.
Smith, who was piloting the aircraft, crashed it into trees. Both survived, but Greene broke both her legs and an arm, while Smith suffered a broken back and ankle.
Last night a spokesman for Smith’s helicopter aerial filming company Flying TV said: “Mike founded Flying TV ten years ago and the company says his legacy will be FTV continuing to go from strength to strength.”
DJ and television presenter Read said: “The news is just devastating. Sarah and Mike were a wonderful couple – it is truly horrible to hear.
“I knew Mike as there were only five of us to have presented the Breakfast Show at that time.
“He became a mainstay of Radio 1, was highly successful on television too, and started up his own business which he was very good at.
“I worked with Sarah for a number of years, including around the time of the crash, so I was very fond of them both.
“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.”
Johnny Beerling, the former controller of BBC Radio 1, said Smith was “a wonderful broadcaster, a good lad, and we will miss him”.
He recalled: “On 1 April, 1986, he announced that he would have Prince playing live on his show.
“Everybody got very excited about all of this – but it turned out not to be Prince the rock star, but Prince Edward, who was friendly with Mike.”
Former colleagues last night took to Twitter to pay their respects.
Simon Mayo, who took on the Breakfast Show when Smith left in 1988, said: “Shocked to hear of Mike Smith’s death today. 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.”
Phillip Schofield, who presented Going Live! with Greene, added: “There are no words. My wonderful, bright, funny, thoughtful friend Mike Smith has passed away @RealSarahGreene I’m so so sorry my darling.”
Showbiz veteran Keith Chegwin added: “Very sad news about Mike Smith. A nice man & great broadcaster.”