Les Squires said the musician, who was in his early 80s, died in Basildon Hospital in Essex at 7.30am.
He said: "He had been in and out of hospital recently but sadly this time he did not come out, but he was playing to the end."
Mr Squires said Ball was survived by his partner and his son, Keith, who had joined his father on stage playing with his group The Jazzmen.
He said the musician had continued to perform, having left hospital to play a gig in Germany at the end of January, before being re-admitted.
Ball, who lived in Essex, found fame in the early 1960s with a string of trad jazz hits including Midnight In Moscow which got to number two in the charts on 1961.
The track, which was also a hit in the United States, sold more than one million copies around the world.
He became a well-known face on TV with his band featuring regularly on light entertainment shows. They made numerous appearances on the Morecambe And Wise Show and went on to become the resident band on the popular BBC1 series Saturday Night At The Mill, which was broadcast from Birmingham's Pebble Mill studios.
He achieved his biggest hit with Midnight In Moscow - effectively his signature tune - but other top 10 hits in the early 1960s were March Of The Siamese Children, The Green Leaves Of Summer and Sukiyaki.
Ball was born in Ilford and, after working as a clerk in an advertising agency in his teens, he began to take music lessons.
His early musical career saw him playing in other people's bands, but he went on to form a combo of his own in 1958.
He consciously moved away from the trad jazz repertoire which was experiencing a revival of interest as he launched his band, and he stamped his mark on numerous tunes over the years including tracks such as When I'm Sixty-Four.
Ball recorded and performed for more than half a century, playing around the world and continuing to be one of the UK's best know jazz trumpeters. He often clocked up in excess of 150 shows a year with his group, The Jazzmen.
He would regularly share a stage with other British jazz legends such as John Dankworth, George Melly and Humphrey Lyttelton. And he toured with trumpeter Louis Armstrong, one of the pioneers of jazz, during the late 1960s.
Ball - who had a distinctive and well-groomed moustache and goatee - famously performed at the wedding reception for Prince Charles and Lady Diana Spencer at Buckingham Palace in 1981.
Broadcaster Alyn Shipton, presenter of BBC Radio 3's Jazz Record Requests, paid tribute to Ball today, saying: "Britain has lost one its most charismatic bandleaders, and a figurehead of the trad movement."
He went on: "With his ready grin, mop-haired appearance and upbeat singing and playing, Kenny Ball was one of the most extrovert and cheery figures in British entertainment.
"His chart-topping hits of the 1960s brought jazz to a huge audience, and he was a dazzlingly accomplished trumpeter, with one of the most developed techniques in jazz.
"Amid the bravura cadenzas were subtleties that passed many of his audience by, such as playing complex solos in unison with his clarinettist, and his high note range seemed so effortless that he made light of its difficulty."
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