The Padres plan to use Cano, 39, as a left-handed bat off the bench. Acting manager Ryan Christenson said he could get some occasional starts at second base and designated hitter.
"I've got a lot left in the tank," Cano said. "I know I can still play this game and just go out on top."
Entering Thursday's games, Padres designated hitters were batting .206 with two home runs and 12 RBIs this season. Both home runs came via Luke Voit, who bats right-handed, in Wednesday's 7-5 loss to the Chicago Cubs.
Kim is batting .200/.326/.388, and there is additional need at shortstop because of Fernando Tatis Jr.'s wrist injury and because top prospect C.J. Abrams was optioned back to the minor leagues after struggling earlier this season.
Cano sat out last season while serving his second suspension for performance-enhancing drugs. He batted .195 (8-for-41) this season with one home run, three RBIs and a .501 OPS in 43 plate appearances for the National League East-leading Mets.
He is owed $44,703,297 by the Mets from the remainder of the 10-year, $240 million contract he signed with the Seattle Mariners. He has lost $35,741,935 because of the two drug suspensions.
He will earn a prorated share of the $700,000 minimum with the Padres.
Cano, who was acquired in a multiplayer trade with the Mariners that also sent closer Edwin Diaz to New York, ended up playing 168 games for the Mets, batting .269 with 24 homers, 72 RBIs and a .765 OPS.
An eight-time All-Star, Cano has a .302 career batting average with 335 home runs, 1,305 RBIs and an .842 OPS in 17 seasons. He has 2,632 hits, including 571 doubles.
In a corresponding roster move, the Padres optioned right-hander Dinelson Lamet to Triple-A El Paso.
ESPN's Alden Gonzalez and The Associated Press contributed to this report.