Klemm had one goal and two assists in 38 regular-season games for the Dallas Stars last season. He has 42 goals and 100 assists in 751 regular-season games in a 14-year NHL career.
Klemm made his NHL debut during the 1991-92 season for the Quebec Nordiques, who later became the Colorado Avalanche, and also played for the Chicago Blackhawks before joining Dallas during the 2003-04 season.
The 37-year-old had two goals and an assist during the playoffs as the Avalanche won the Stanley Cup in 1996, and a goal and two assists in the postseason five years later for another championship team in Colorado.
Klemm was coached by current Kings coach Marc Crawford for three seasons in Colorado.