The star, whose rendition of the song made him world famous, passed away following a year-long battle with bladder cancer on Tuesday.
Williams won a legion of fans around the world with his easy-listening style and smooth vocals. He started singing with his brothers as a child and had more than 20 hit singles over 50 years, including Music To Watch Girls By and Can't Take My Eyes Off You.
DJ Tony Blackburn said he had "so many great songs", adding: "One of the best concerts I ever went to was Andy Williams at the Royal Albert Hall, he was tremendous."
Charlatans frontman Tim Burgess said: "Another sad loss. Andy Williams was a real smooth guy, that's for sure".
Fellow crooner Tony Christie described Williams as "a very charming man" who had "perfect pitch". Actress Liz Hurley tweeted: "RIP Andy Williams – thanks for the wonderful songs which you gave to the world." He is survived by his widow, Debbie, and his three children.