The incident occurred shortly before 9 p.m. when the driver slowed the van to a crawl in a northbound lane near East Avenue 43 and climbed through the driver side window, landing on the freeway's center median.
The driver rolled off the median and onto the southbound side of the freeway, where he was immediately struck by a vehicle.
Police and firefighters quickly arrived at the crash site, and paramedics were seen administering CPR to the suspect, who was lying in a center lane.
The suspect was pronounced dead at the scene.
Details of where and when the van was allegedly stolen were not immediately available.
The Los Angeles Police Department initiated the chase and requested the California Highway Patrol to take over after the van entered the 110 Freeway.
Whether one or both agencies were involved in the pursuit when the suspect exited the van was unclear.
The freeway closure was in effect for several hours. The CHP said it was reopened shortly before 2 a.m. Tuesday.