The Londoner had previously failed in bids to win the WBA super-middleweight title on three occasions, but a technical knockout during an action-packed bout against the former champion saw him achieve his dream at the fourth time of asking.
Both fighters came out exchanging punches from the very first bell, with Groves the early aggressor but also allowing Chudinov to land some heavy shots.
The fight moved up another notch in the fourth round when Groves sustained a cut to his left eye following an accidental clash of heads, but the 29-year-old responded and hurt Chudinov with some big right hands.
That was the beginning of the end of Chudinov and the referee eventually stepped in during the sixth round as Groves began to inflict more punishment on his opponent.
Groves now claims the previously vacant WBA super-middleweight belt, which had been held by Felix Sturm before he relinquished it due to an injury.