CLEVELAND — The Golden State Warriors launched some 8,900 shots this season. They attempted layups and 3-pointers, runners and elbow jumpers. They dazzled fans and overwhelmed opponents. But every time the ball left their fingertips, the Warriors seemed to be building toward something bigger and better, toward the brightest stage and the grandest prize.

The Warriors were chasing history, a journey they completed Tuesday at Quicken Loans Arena with a 105-97 victory over the Cleveland Cavaliers in Game 6 of the N.B.A. finals.

Golden State celebrated its first N.B.A. championship in 40 years when the final buzzer sounded, the players forming a frantic mob at center court as silence fell over the sellout crowd. The Warriors won the final three games of this best-of-seven series, countering every move that the Cavaliers made — and all the points, rebounds and assists that LeBron James could produce.

“Pure joy,” said Steve Kerr, the coach of the Warriors, who showed up to his news conference soaking wet, fresh off a champagne shower in the locker room.