Sweet: One of the leading bands of the early 1970s
He died in hospital in Welwyn Garden City, Hertfordshire, on Thursday after a five-year battle against leukaemia, his US agent Maureen O'Connor said.
His wife Janet and daughter Aysten, 22, were at his bedside.
The Sweet was one of the leading bands of the hell-raising glam rock music era, securing top 10 hits with Fox On The Run, Blockbuster and Hell Raiser.
Another hit, Ballroom Blitz, featured in the 1992 movie Wayne's World, giving the band a resurgence in popularity.
Fellow band member Steve Priest - played bass guitar - paid tribute to his friend of 30 years.
"He was the best drummer England ever produced and it is a sad loss to the music world," said Priest.
Speaking from his home near Los Angeles, Priest, 53, added: "It was a little bit sudden, to be honest.
"He was on the verge of leukaemia five years ago but had a bone marrow transplant from his brother which stopped him getting it, but he was never the same."
Priest added: "He was supposedly clear of it but he had a job fighting infections."
Tucker, who lived in Chorleywood, Hertfordshire, died from complications of the cancer, according to his agent.
Outrageous
Sweet were made up of four members, the other two being lead singer Brian Connolly and Andy Scott, who was also on vocals, keyboard and guitar.
The band formed in 1968 as Sweetshop and went on to become Sweet - one of Britain's most successful bands of the next decade.
Like many of the stars of the glam rock movement, Sweet revelled in outrageous costumes, make-up and a fast-living lifestyle.
By 1973, the blatant nature of their lyrics and overt stage antics led to some British clubs banning them.
The way of life led by the band members, involving, above all, excessive amounts of alcohol, took its toll, particularly on Connolly.
He died of liver failure in 1997, while the fourth original member of the band, Andy Scott, lives in Britain.