"Jelle is an experienced, talented defender who will strengthen our back line," Galaxy head coach and general manager Bruce Arena said in a statement.
"He joins our team with a wealth of experience playing at the highest levels of competition in the world. We look forward to adding him to our roster."
The globe-trotting Van Damme, 32, who previously played for Standard Liege and has represented his country 30 times since his debut in 2003, is expected to replace United States international defender Omar Gonzalez at centre back.
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Gonzalez, the MLS Rookie of the Year in 2009, was transferred by the Galaxy last month to C.F. Pachuca in Mexico's Liga MX.
(Reporting by Mark Lamport-Stokes; Editing by Pritha Sarkar)
