The guaranteed deal includes a club option for a third year, the source said.
The Angels also bolstered their bullpen Wednesday, agreeing to a two-year contract with left-handed reliever Sean Burnett.
Financial terms of Burnett's deal, which is pending a physical, were not immediately available.
The addition of Blanton, coupled with last week's acquisition of Tommy Hanson in a trade with Atlanta, appears to make it less likely the Angels will bring back free agent Zack Greinke, who is being pursued aggressively by both the Los Angeles Dodgers and Texas Rangers.
Blanton, who turns 32 next week, is 83-75 with a 4.37 ERA in nine seasons with Oakland, Philadelphia and the Dodgers. He went 10-13 with a 4.71 ERA while splitting the 2012 season between the Phillies and Dodgers. Blanton walked just 34 batters in 191 innings, but also allowed 29 home runs.
The Minnesota Twins were among the other clubs that had been talking to Blanton.
Burnett, 30, has a 15-23 record with a 3.58 ERA in six seasons with Pittsburgh and Washington. He has logged 73, 69 and 70 appearances, respectively, with the Nationals in the past three seasons.
Burnett has held left-handed hitters to a .225 batting average and a .628 OPS during his career.
During the past week, Angels general manager Jerry Dipoto has added Burnett and Ryan Madson to his bullpen through free agency.