The Saint, fighting for the first time since his defeat to Carl Froch at Wembley Stadium in the summer, was keen to impose himself on his French opponent, working behind his jab and was able to unload shots in the early rounds as Rebrasse struggled to move.
Groves continued to dominate behind the jab in rounds three and four as the former champion relied on his stubbornness to stay in the fight, but failed to land enough significant blows of his own.
It became clear that the challenger, in front of what was a partisan crowd at Wembley Arena, was boxing more cautiously with sporadic burst of punches after a high-tempo start in the first four rounds.
Rebrasse continued to take shots and remained in the fight, but was not able to lull Groves into a mistake, with the Englishman's corner repeatedly urging their man not to try too hard for a knockout.
Groves appeared to heed the advice from his corner and fought patiently as Rebrasse could not find any killer blow to down the home fighter and, inevitably, the challenger won by a unanimous points decision to take the belt.
The victory also served a potential title eliminator for a shot at the WBC crown currently held by Anthony Dirrell, with a mooted match for Groves as early as the end of 2014.