Bobby Hackett was born in Providence, Rhode Island. He made his name as a follower of the legendary cornet player Bix Beiderbecke. Benny Goodman hired him to recreate Bix's famous "I'm Coming Virginia" solo at his (Goodman's) 1938 Carnegie Hall concert.
In the late 1930s Hackett played lead trumpet in the Vic Schoen Orchestra which backed the Andrews Sisters. Hackett can be heard on the soundtrack to the 1940 Fred Astaire movie Second Chorus. In 1939 the talent agency MCA asked Hackett to form a big band with its backing. Unfortunately the band failed and Hackett was in substantial debt to MCA after it folded. Hackett joined the bands of Horace Heidt and then Glenn Miller to pay down this debt. To make matters worse, his lip was in bad shape after dental surgery, making it difficult for him to play the trumpet or cornet. Glenn Miller came to Hackett's rescue, offering him a job as a guitarist with the Miller Band. "When I joined the band and I was making good money at last, [...] [jazz critics] accused me of selling out. Hell I wasn't selling out, I was selling in! It's funny, isn't it, how you go right into the wastebasket with some critics the minute you become successful". Despite his lip problems, Hackett could still play occasional short solos, and he can be heard playing a famous one with the Glenn Miller Orchestra on "A String of Pearls".
A dream come true for Hackett was his inclusion in Louis Armstrong's 1947 Town Hall Jazz Concert. In 1954, Hackett appeared as a regular on the short-lived ABC variety show The Martha Wright Show, also known as The Packard Showroom.
However, what made Hackett something of a household name was his being hired by Jackie Gleason as a cornet soloist for some of Gleason's earliest mood music albums. Starting in 1952, Hackett appeared on Gleason's first Capitol Records album, Music for Lovers Only. The record – as well as all of Gleason's next 10 albums - went gold. Hackett went on to appear on six more Gleason LPs. This association led directly to Hackett signing with Capitol for a series of his own albums.
In 1965, he toured with singer Tony Bennett. In 1966 and 1967 Hackett accompanied Bennett on two European tours. In the early 1970s, Hackett performed separately with Dizzy Gillespie and Teresa Brewer. In 2012, Hackett was selected to be inducted into the Rhode Island Music Hall of Fame.