Pineiro is due to take a physical Thursday.
Pineiro, 31, pitched a career-high 214 innings over 32 games last season, with a 15-12 record and 3.49 ERA for the National League Central champion St. Louis Cardinals. He has an 87-79 record with a 4.39 ERA in 10 major league seasons that also included a stint with the Red Sox.
The Mets and Dodgers also were believed to have interest in Pineiro.
Messages left with Angels general manager Tony Reagins were not immediately returned. One of Pineiro's agents, Arn Tellem, had no comment when reached by ESPNLosAngeles.com on Wednesday night.
The Angels were in the market for a starting pitcher after ace John Lackey signed a five-year, $82.5 million deal with the Boston Red Sox last month. Pineiro would appear to be an upgrade over the Angels' in-house candidates, led by journeyman right-hander Matt Palmer.
Now that Pineiro is bound for the Angels, the Dodgers are expected to focus on signing free-agent right-hander Vicente Padilla.
The Dodgers have been talking to Pineiro, Padilla, Jon Garland and Braden Looper. But money remains an issue. And Padilla is likely to be willing to sign a one-year deal for a relatively low base, plus incentives.
Padilla went 4-0 in seven regular-season starts for the Dodgers down the stretch last season, then made two spectacular postseason starts (1-0, 0.63) before getting raked for six runs in three innings against the Phillies in Game 5 of the NL Championship Series.
Information from ESPN The Magazine senior writer Buster Olney, ESPNLosAngeles.com's Mark Saxon, ESPN.com's Jayson Stark and The Associated Press was used in this report.