"I always said what I would do and I delivered. I didn't have this confidence for nothing," beamed Fury, 27, after his unanimous points win ended Klitschko's run of 19 consecutive defences.
Fury was awarded the fight in Duesseldorf 115-112, 115-112 and 116-111 by the judges on Sunday (AEDT) as Klitschko's reign as world champion was ended after nine years, six months.
He's been a great champion, but every good dog has its day. This is that start of a new era. I'll be the most charismatic champion since Muhammad Ali.
World heavyweight boxing champion Tyson Fury
"People can say what they want about me, he was hanging on for dear life in that fight all the way through," Fury said.
"He's been a great champion, but every good dog has its day.
"This is that start of a new era. I'll be the most charismatic champion since Muhammad Ali."
The new champion celebrate his victory by singing Aerosmith's Don't Want to Miss a Thing in the ring.
"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 pounds ($417,910) on himself.
He made good on his pre-fight predictions of dethroning Klitschko and even took to song last Wednesday to tell the champion how he would "be the one with all the belts" after the bout.
The fight took place at the second attempt as the original October date had to be scrapped after Klitschko suffered a calf injury.
Fury had made the headlines in September at a press conference for the original scheduled fight when he turned up dressed in full superhero costume as Batman.
The two men wrestled on the ground before Fury "won" - he then called out Klitschko, saying the Ukrainian would end up on his back the same way as the unknown intruder.
After Fury had problems with ill-fitting gloves in the week leading up to the fight, there was plenty of tension in the build-up to the fight.
Fury's management insisted the canvas was too soft and after much discussion and threats to call the fight off, Klitschko's camp relented and removed some of the foam padding from the ring floor.
Then Klitschko was reported to have had his fists wrapped without an observer being present, a no-no in boxing, and when Fury's camp complained, the champion's fists were re-strapped which briefly delayed the start of the fight.
This was a poor display by Klitschko who finished with cuts to both cheeks with Fury unmarked.
The Briton showed no sign of nerves in a confident start, lowering his guard and trying to lure Klitschko inside his huge reach.
There was little between the fighters in the opening four rounds, as Klitschko struggled to impose himself, while Fury opened up a small cut on the champion's left cheek in the fifth with a jab.
The fight burst into life in the seventh round in a flurry of punches from Fury, who even put his fists behind his back at one stage, which left Klitschko's cheek showing more signs of punishment and in clear trouble.
A big left from Fury caught Klitschko flush in the face in the ninth round before the champion finally got his right-hand jab going as he went on the attack and landed a shot directly on Fury's chin.
Fury, who landed a good shot to the right eyebrow, had a point deducted in the 11th for punching the back of Klitschko's head despite several warnings.
Klitschko came out hard in the 12th and looked for the knock-out as Fury visibly tired, but both raised their fists in triumph at the final bell