Earlier this week, Greinke opted out of the final three years of his contract, giving up a guaranteed $71 million to become a free agent. The 32-year-old right-hander was 19-3 with a major league-best 1.66 ERA this season, when he struck out 200 in 222 2/3 innings.
Second baseman Kendrick was acquired last winter from the Angels in a trade that sent second baseman Dee Gordon to Miami.
The Dodgers declined club options on Bronson Arroyo, Joel Peralta and Chase Utley, who all became free agents. Chris Heisey and Justin Ruggiano elected free agency.
Arroyo, a former All-Star, didn't pitch this season while recovering from Tommy Brice McCain JerseyJohn surgery. His option was worth $13 million with a $4.5 million buyout.
Peralta, acquired last winter from Tampa Bay, was 3-1 with a 4.34 ERA in an injury-riddled season. His option was worth $2.5 million.
Utley, who was acquired from Philadelphia to fill in for Kendrick after he was injured, hit .202 in 34 games. He will be best remembered for his takeout slide that broke the leg of Mets shortstop Ruben Tejada in the NL Division Series. His option was worth $11 million with a $2 million buyout, which the Phillies agreed to reimburse the Dodgers as part of the trade.
Ruggiano was sent outright to Triple-A Oklahoma City by the Dodgers, who needed to clear a roster spot. Ruggiano would have been eligible for salary arbitration if he had remained on the team's 40-man roster and been offered a contract by the Dec. 2 deadline.
He was acquired from Seattle on Aug. 31 and filled in for injured outfielder Yasiel Puig. Ruggiano batted .291 in 21 games with the Dodgers, going 0 for 4 with three strikeouts in the postseason.