The 23-year-old Mancunian, who has won all his 17 professional bouts, will instead target a world title.
Fury said: "It's been an honour to have won and held both the British and Commonwealth heavyweight titles, but as I'm now currently number number seven in the world it's time to move on ...
"I'm really excited about my future plans as I'm doing things differently and currently training like a Trojan in pursuit of becoming heavyweight champion of the world."
The fight ends the prospect of Fury meeting domestic rival David Price.
And Price's promoter Frank Maloney has christened Tyson 'Chicken Fury'.
Maloney said: "Chicken Fury was going to get the biggest pay of his career to date, and has let himself, his fans, his traveling community and most of all the boxing world down.
"This is why people are turning against the sport I love and again politics have ruled what a boxer does."
"The BBBofC have purse bids for a reason and this fight generated more interest than normal with all the top promoters in the UK bidding for it."
"Hennessy sent out a statement this morning saying that Fury will be pursuing world titles - but the nearest Fury will get to winning a world title is having the same nickname as former WBC heavyweight champion Riddick Bowe who was christened 'Chicken Bowe' for also clucking away from another British Olympian.
"Chicken Fury will regret the day he gave up his belts and the chance to earn his biggest pay to date."
Fury's promoter Mick Hennessy countered and said: "We have a great schedule in place for Tyson on Channel 5 and I'm not prepared to have that affected by other promoters, purse bids and titles.
"Fury versus Price was a quality fight and in my opinion it should go out to the widest possible audience, that's why I offered David Price £100,000 to fight Tyson Fury on Channel 5, which unfortunately was rejected by his promoter on Monday."