Kaman averaged 10.5 points and 5.6 rebounds while starting 52-of-66 games for Dallas last season. He averaged a career-low 20.7 minutes.
His one-year deal with the Lakers is worth the team's mini mid-level exception amount of just under $3.2 million, sources previously told ESPN.com.
"We're pleased to be able to add a big man of Chris' caliber to the roster for the upcoming season," Lakers general manager Mitch Kupchak said in a statement. "He's a versatile center who defends well, goes hard to the glass and can score both in the paint and from mid-range while also being a high character guy and solid locker room presence."
It will be Kaman's second straight season on a one-year contract. He had an $8 million deal to be the starter in Dallas last season but spent more than half of every game on coach Rick Carlisle's bench.
The 10-year NBA veteran has also played with the Clippers and New Orleans in his career.
Kaman made the 2010 All-Star team. As a dual citizen of the U.S. and Germany, he played for the German team at the 2008 Beijing Olympics.
Information from ESPN.com's Marc Stein, ESPNLosAngeles.com's Ramona Shelburne and The Associated Press was used in this report.