The closure began at 8 p.m. with California Highway Patrol officers running traffic breaks on the bridge to stop vehicles from crossing, CHP Officer Sam Morgan said.
Crews were set to begin final work on the new span, which is scheduled to open by 5 a.m. Tuesday, or possibly earlier if the work is done ahead of schedule, Metropolitan Transportation Commission spokesman John Goodwin said.
During the closure, BART is running longer trains on Thursday and Friday and providing 24-hour service at more than a dozen stations.
BART officials say they expect a surge in ridership, noting that during previous Bay Bridge closures, trains have carried 30 percent more passengers than usual.
The CHP expects traffic to increase on other Bay Area bridges and advised drivers to expect delays.
"Allowing yourself additional time to get to your destination would be a wise thing to do," Morgan said.
Golden Gate Ferry service is being boosted this Labor Day weekend from Larkspur and Sausalito into San Francisco, and San Francisco Bay Ferry is adding ferries between the East Bay and San Francisco.
Alameda-Contra Costa Transit buses that normally take riders across the bridge will instead go to the MacArthur, Oakland Coliseum, West Oakland and North Berkeley BART stations, agency officials said.
A low-key ceremony celebrating the opening of the new eastern span is tentatively scheduled for 3 p.m. Monday.
A large-scale, public celebration had initially been in the works, but the plan was scrapped after problems with anchor bolts on the new span left the bridge's opening date in limbo.
A temporary fix was since devised to cover the broken rods with an exterior saddle and cable system encased in concrete.
The old eastern span, a cantilever bridge that opened in 1936, has been slated for replacement since the 1989 Loma Prieta earthquake, which caused a section of the span's upper deck to collapse.
Bay Area residents and visitors are advised to call 511 or visit alert.511.org to learn about all of the options for getting around during the closure.