The deal will become complete when Pierre passes a physical exam, the source said.
Pierre, 29, is a .303 hitter over seven seasons with Colorado, Florida and the Chicago Cubs. He led the National League with 204 hits in 2006.
"He's another guy with great qualities as a human being, like
Nomar [Garciaparra]," Dodgers general manager Ned Colletti told the Associated Press.
Colletti wouldn't confirm the deal with Pierre.
"It's either done or it's not done and right now it's not
done," Colletti told AP.
The San Francisco Giants were also interested in Pierre, and had offered him a four-year deal in the $32-34 million range, a source said.
Jerry Crasnick covers Major League Baseball for ESPN Insider.