The Angels won their first World Series title in 2002 by beating the San Francisco Giants in seven games.
Two charter buses were given a police escort to 1600 Pennsylvania from the team's hotel in Baltimore, where the Angels played the Orioles on Tuesday night.
The President made all attending the Rose Garden ceremony feel at ease with several jokes and a good nature.
One of the players on his hit list was popular shortstop David Eckstein, one of baseball's smallest players, who had already met the President in an offseason dinner he hosted with columnist George Will.
"I understand some of the players were so excited that, well, like David Eckstein, who actually went out and purchased a suit," he cracked. "Fine looking."
The President also had a congratulatory salute for Arte Moreno, the new team owner and first of Hispanic descent, who attended the ceremony with his wife, Carole.
"I really want to congratulate the team owners," Bush said. "First, I want to congratulate you, Arte, for being an owner of the team. It's pretty quick how things happen here in America. You buy the team, now you're at the White House."
He also paid tribute to the late Gene Autry, known as The Singing Cowboy when he was an actor, and the former owner, who died in 1998. He bought the Angels in 1983.
"Gene was the owner of the team when I was fortunate to be in baseball, and he's an amazing guy," Bush said. "I know that he's smiling down now here, looking at the Rose Garden and realizing his beloved Angels have finally won the world championship."
Bush served as Managing General Partner of the Texas Rangers from his purchase of the team in 1989 until his election as governor of Texas in November 1994.
He was reminded of that by Anaheim Manager Mike Scioscia.
"Mr. President, it took us 42 years to say this, but we'd like to present you with a world champion Anaheim Angel jersey that I know you'll wear proudly," Scioscia said. "And we apologize for going through your beloved Texas Rangers in the American League West."
The jersey he was given had the No. 1 on it.