Captain Landon Donovan scored the only goal of the match in the 72nd minute, cleverly lifting the ball over an advancing goalkeeper as the Galaxy claimed their first championship since 2005 and third in the past decade.
"It's a sense of elation," Donovan told a news conference after being named the match's Most Valuable Player (MVP).
"I've been so determined to win this and I just wanted the ball to go in, it didn't matter who scored. It's been a trying year.
"Winning feels so good."
The Galaxy deserved the victory after dominating the contest to secure a title victory that validates the franchise's lucrative investment in a star-studded line-up.
With Beckham, who arrived in 2007, Irish striker Robbie Keane and Donovan in the squad, the side has three 'designated players' paid above salary cap restrictions and anything less than a title victory would have been deemed a failure.
The Galaxy's win marks the first MLS title for a team with a designated player and may signal a new era of star power for the league.
After capturing the Supporters' Shield for the best record in the regular season, it was perhaps fitting that the team's three big-name players rose to the occasion by combining for Donovan's well-taken goal.
The winning attack started with Beckham winning an aerial battle by heading forward to Keane, whose defence-splitting pass put Donovan through on goal and the U.S. international calmly slotted the ball past an advancing Dynamo keeper Tally Hall.
It was the kind of sequence the Galaxy had envisioned when they signed Keane in August to combine with the team's other leading lights.
Captain Brian Ching did his best to create chances for the visitors, who were playing without injured striker Brad Davis, and the Dynamo defence stood firm to hold the Galaxy at bay for long periods.
Los Angeles thought they had scored the opening goal a few minutes before Donovan's winner when Keane completed a sweeping move but was flagged offside, with television replays suggesting the Irishman was level with the final defender.
Despite the defeat, it was a strong campaign for the Dynamo, who overcame a slow start to the season and made a convincing playoff charge before running into the overpowering Galaxy.
"They've been the best team in the league from the first day until now," said Dynamo coach Dominic Kinnear of the Galaxy.
"They're a deserving champion."
