He named a veteran Republican lawmaker on Wednesday as his transition chief and reached out to his severest critics, top Democrats who fought tooth and nail to prevent his election.
The governor-elect also pledged to move quickly to tackle the state's dire financial plight while sticking by his campaign promise not to raise taxes.
"We don't know exactly what the current operating deficit is. It went from $7 billion to $8 billion to $10 billion and just this morning I found out if this court case goes wrong, it could go to $20 billion," he told a news conference.
He was referring to a previously announced lawsuit that would stop the state from issuing bonds aimed at helping to fund the current state deficit.
In his first news conference since sweeping to victory in Tuesday's election, the bodybuilder-turned-movie star repeated pledges to repeal an increase in the state vehicle tax, promote business growth and reverse legislation granting illegal immigrants the right to receive driver's licences.
Schwarzenegger named David Dreier, a 12-term US congressman from southern California, to head his transition. He said Dreier would announce the rest of the team and its plans on Thursday.
Terminator star must revive state
finances while keeping foes at bay
Dreier is best known as an aggressive proponent of free trade and tax reductions and a believer in removing taxes and regulations on business.
Schwarzenegger also accepted congratulations from President George Bush, former President George Bush senior and former South African President Nelson Mandela, among many others. He took several of the calls while working out on an exercise bike.
He said he would put his movie career on hold to work around the clock for the state.
After sweeping to decisive victory in the unprecedented recall election, Schwarzenegger reached out to virtually every top Democrat in the state.
Ousted governor Gray Davis (L)
paid the price for budget crisis
He said he had spoken to Democratic senators Dianne Feinstein and Barbara Boxer and State Senate President John Burton to help make his first 100 days in office as smooth.
Feinstein, who waged a strong campaign to help her one-time foe Davis remain in office, said she was ready to help Schwarzenegger and called a rumored Democratic effort to subject him to a recall drive a "mistake".
"One of the problems is hyper-partisanship," Feinstein said. "You need to break that cycle."
His first task is to craft a budget by January that addresses the yawning deficit for the next fiscal year. Most of California's budget goes to education, social programs, law and order and prisons.
But Schwarzenegger may find himself with little room for manoeuvre and forced to cut popular programs to balance the budget, which the state is obliged to do by law.
Burton, whose tenure in California politics goes back to the days when Ronald Reagan was governor, said Schwarzenegger may have to think twice about his pledge not to raise taxes.
"If he tries to raise taxes the Republicans will have him for lunch ... My judgment is Mr Schwarzenegger may have more trouble with the Republicans than the Democrats," he said.
A political debutant, Schwarzenegger easily won the governorship in a recall election on Tuesday that saw voters angry at the state of the economy. With virtually 100% of ballot stations reporting, 55.2% of voters said yes to the recall while 44.8% voted no.
In the section of the ballot where voters were asked to choose a replacement, Schwarzenegger led his nearest rival by 48.5% to 31.8%.