He had no goals, three assists and 12 penalty minutes in 26 games with the Washington Capitals last season.
The Kings announced the deal Friday as the NHL's free agency period began.
Schultz has spent his entire NHL career with the Capitals, with 11 goals, 64 assists and 133 penalty minutes in 399 games. He was drafted by the team in the first round of the 2004 NHL entry draft. During the 2011 playoffs, Schultz set a league post-season record by being on the ice for 119 consecutive minutes without his team being scored upon.