The 27-year-old Fury was awarded the fight in Duesseldorf 115-112, 115-112 and 116-111 by the judges to take Klitschko’s WBA, IBF, IBO and WBO belts as the Ukrainian suffered his first defeat since 2004.
The new champion celebrate his victory by signing Aerosmith’s “Don’t Want to Miss a Thing” in the ring.
“I want to thank my lord and saviour Jesus Christ for giving me this victory,” said a tearful Fury who has now won all 25 of his professional fights.
“I have worked hard everyday for this moment, it’s a dream come true.”
Klitschko said there is a rematch clause in the fight contract, adding it was too soon to talk about retirement and admitted he was surprised by Fury’s speed despite his towering 2.06m frame.
“I prepared well, but my speed was missing tonight and I didn’t expect the speed from him,” said Klitschko, who turns 40 in May.
“I knew I needed a knock-out at the end,” he added after his fourth professional defeat.
Fury will cash in on the victory regardless of the fight purse having bet £200,000 on himself.