Breakfast Show alumni including Noel Edmonds, Mike Read and Simon Mayo joined others from the world of entertainment in mourning Smith's death.
Smith, who was married to fellow television personality Sarah Greene, died in hospital on Friday from complications connected to his recent major heart surgery. The couple, who married in 1989 and were childless, lived in London.
Edmonds, a long-term friend of the couple, said in a statement: "I am totally stunned and heartbroken for Sarah and his family. He was so much more than simply a presenter. 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."