The Kings announced the deal Wednesday with Kempe, a restricted free agent who turns 23 next week.
Kempe had 12 goals and 16 assists in 81 games last season for the Kings, the NHL's second-lowest-scoring team with just 199 goals.
The Swedish two-way center scored 37 points during the 2017-18 season, his first full NHL campaign. The Kings expect Kempe to increase his offensive productivity under new coach Todd McLellan, team President Luc Robitaille said.
"He's played a certain role with our organization, and I think this year he sensed that he's got probably a little more of an offensive role he's going to have to fulfill," Robitaille said. "That's going to really give him a chance to create and get more chances. Usually goals come with chances. He's been doing really good at checking and so forth, and we're looking for him to help on the other side, too."
Kempe has been playing center for most of his short NHL career, but has the versatility to move to a wing in the future. He has won just 41% of his career faceoffs.
Kempe was the Kings' final unsigned free agent. Los Angeles opens training camp next week.