The move comes five weeks after state lawmakers failed to act on a billion prison construction plan Schwarzenegger sought after calling a special session of the Legislature.
"Our prisons are now beyond maximum capacity, and we must act immediately and aggressively to resolve this issue," Schwarzenegger said in a statement.
California has the nation's largest state prison population with 172,000 inmates. Its prison system is about 70 percent over capacity. Without swift action, the prisons will run out of bed space as early as June, according to the state Department of Corrections and Rehabilitation.
Privately operated prisons in Arizona, Indiana, Oklahoma and Tennessee are willing to take 2,200 inmates, Corrections Secretary James Tilton said. Transfers could start in 30 days.
Other prisons, public and private, are interested in providing as many as 10,000 beds for three to five years, he said.
A preliminary survey conducted by prison officials last month found that nearly 20,000 inmates are willing to be shipped out of California, more than enough to meet an initial goal of 5,000 transfers.
"If I was living in a gym with 240 other individuals and had no programs, then I'd probably raise my hand, also," Tilton said.
Schwarzenegger's order permits Tilton to move convicts against their will if needed, starting with foreign nationals who would be deported after their release.