He joins his younger brother, Jered, a former pitching star for Long Beach State, who is a prospect in the Angels' organization.
"It's another quality arm that we're getting in here," Angels pitcher John Lackey said. "You never can have too much pitching."
Weaver, scheduled to report Thursday, can earn an additional $600,000 in performance bonuses: $300,000 each for 200 innings pitched and 32 starts as a pitcher.
He went 14-11 with three complete games, two shutouts and a 4.22 ERA in 34 starts last season with the Dodgers, earning $9.35 million in the final season of a four-year contract.
The 29-year-old right-hander was eighth in the NL in starts and innings (224) and sixth in complete games. He also had 157 strikeouts and 43 walks, a ratio of 3.65 that was eighth in the league. He set career highs in wins, strikeouts and fewest walks, and tied his mark for starts.
Weaver also had a career-best six straight victories from July 22-Aug. 28 and pitched into the seventh inning in 18 consecutive starts from May 24-Aug. 28, another career high.
Lackey, 14-5 a year ago, won't have to worry about being pushed out of the rotation, but newcomer Hector Carrasco may have to compete for a spot. The right-hander, 5-4 with a 2.04 ERA in 64 games with Washington last year, signed with the Angels with the hopes of settling into one of the five spots in the rotation.
"I signed as a starter," said Carrasco, impressive in five starts late last season. "I've been in the bullpen a long time. I can do anything. Whatever they want me to do, I'll do."
Weaver has a 78-87 career record, with 13 complete games, five shutouts, two saves and a 4.44 ERA in 226 major league games, including 209 starts.
He pitched for the Tigers from 1999-2002, the New York Yankees from 2002-2003 and the Dodgers the past two seasons. He has appeared in the postseason twice, for the Yankees in 2002 and 2003,
and the Dodgers in 2004.
Weaver figures to join a rotation that will include Lackey and Cy Young Award winner Bartolo Colon (21-8, 3.48). Young Ervin Santana posted a 12-8 mark in 23 starts after being called up from the minors.
Carrasco and Kelvim Escobar may duel for the fifth spot. Escobar, like Carrasco, has been back and forth between the starting rotation and the bullpen in recent years. He had a 3-2 mark in 16 games (seven starts) in an injury-plagued 2005 season.