The deal is pending a physical exam, the source said.
Kendrick joined the Dodgers last season, staying in Los Angeles after being traded in the 2014 offseason by the Angels, for whom he played nine seasons. He batted .295 with nine home runs and 54 RBIs in 2015.
The Dodgers had extended a one-year, $15.8 million qualifying offer to Kendrick after the season, but he declined it. The Dodgers would have received a compensation-round draft pick if Kendrick had signed elsewhere.
Kendrick's return seemingly solidifies second base for the Dodgers, whose other options are Enrique Hernandez and veteran Chase Utley, who was re-signed to a one-year, $7 million deal last month. Utley could back up third baseman Justin Turner, who is recovering from surgery on his left knee in October.
Fox Sports first reported that Kendrick was re-signing with the Dodgers.
Information from ESPN's Buster Olney and Mark Saxon and The Associated Press contributed to this report.