Chisora rocked Fury in the second round with a left and two further rights but it was the only time the champion looked like he might win the fight.
Fury, 23, looked fresh throughout and picked his opponent off at ease to earn a wide unanimous decision.
Two judges scored the fight 117-112 with the other scoring it 118-111.
"This is a dream come true and it means the world to me," said Fury.
Victory for the unbeaten Fury -  the 15th of his professional career  - could now open the door to a potential world title shot against either of the Klitschko brothers.
Wladimir Klitschko, WBO, IBF and WBA champion, openly discussed the prospect of facing the winner in the build-up to the Wembley Arena showdown, and now Fury can dream of a shot at the big time.
This is a dream come true and it means the world to me
Chisora has had two proposed bouts with Ukrainian Klitschko cancelled within the past eight months but he looked a long way short of a fighter ready to mix in such exulted company.
Manchester's Fury started the fight on the front foot and looking sharper than 27-year-old Chisora, who looked rusty and like a boxer that had not fought for nearly a year.
And certainly Chisora's pre-fight weight of 18st 9lb - the heaviest of his career - seemed to suggest the Finchley-based boxer had taken a less than professional approach to training for the fight.
It was the Fury jab that proved the most effective punch, with his short clubbing left also finding the target throughout.
The previously unbeaten Chisora rocked Fury in the second and had his man in trouble in the third and fourth but the challenger cleared his head and dominated from there on in.
Fury boxed well throughout, throwing some beautiful combinations while never looking like ending the fight early, with Chisora cutting a battered, bloodied and disheartened figure as the fight wore on.
At one stage his corner threatened to pull Chisora out of the fight in an attempt to spark him into life, but it made little difference.
He was constantly worn down by Fury's physical dominance and relentless work rate and despite a 30-second burst from Chisora in the 10th, he never looked liked turning the fight around.
The champion knew he needed a stoppage in the final round but he lacked energy and intensity as Fury managed to keep the disappointing Chisora at length to take the fight and British and Commonwealth titles on points.
Ashley Theophane overcame a difficult start to stop Welsh veteran Jason Cook in the 10th round of the first defence of his British light-welterweight title at Wembley Arena.
Cook, whose career record slips to a potentially final 28-4-1, unsettled the Londoner early on with some intelligent pressure fighting and Theophane's frustration was clear when he was docked a point for low blows in round five.
But the champion, now 30-4-1, regrouped, finding his range with a number of sharp combinations before flooring his foe conclusively with a left hook to the body in round 10.
Tyson Fury defeated Dereck Chisora on points to become the new British and Commonwealth heavyweight champion after a brutal fight at Wembley Arena.