It was the second major announcement in two days for the actor. On Wednesday, the campaign said billionaire investor Warren Buffett would be a financial adviser.
Buffett and Shultz will be joint co-chairs of the economic council. The appointments of Buffett, a Democrat, and Republican Shultz reflect the campaign's attempt to assemble a diverse and bipartisan team.
The campaign will soon have an economic summit, Schwarzenegger told reporters in brief remarks on his way into a San Fernando Valley middle school where he attended a commencement ceremony for an after-school program he's involved with.
It was Schwarzenegger's first exchange with reporters since he filed candidacy papers Saturday, and his first public appearance since attending a summer school program in New York on Monday.
``I'm a very astute businessman. I know exactly what I'm doing,'' Schwarzenegger said of his qualifications to govern California. He cited his involvement with Proposition 49, the after-school programs ballot initiative he successfully championed last year.
He also responded to comments earlier in the day by Arianna Huffington, one of his 134 opponents to replace Democratic Gov. Gray Davis if he is removed in the Oct. 7 recall election.
With President Bush arriving in California for a two-day visit, Huffington branded Schwarzenegger a ``Bush Republican through and through.''
``It doesn't matter what Arianna or anybody says,'' Schwarzenegger said.
Huffington also criticized Schwarzenegger for meeting with former Enron Chairman Ken Lay in May 2001 in Beverly Hills. The Los Angeles Times reported at the time that Lay gave Schwarzenegger and other business and political leaders, including then-Los Angeles Mayor Richard Riordan, a four-page plan detailing his solution to California's energy crisis.
``I don't remember the meeting,'' Schwarzenegger said.
``Do I remember all the meetings that I had in the last decade?'' he said.
``Well you know that I'm not responding to any of those things because I would be crazy if I would,'' Schwarzenegger said. ``To me the most important thing is that we move forward in a positive way. My campaign is a positive campaign that will bring the economy back, reduce the budget and teach the politicians in Sacramento that we cannot go and spend money that we don't have.''
After the exchange, he went inside Mulholland Middle School, where he sat for about 25 minutes with students and parents, watching the commencement ceremony.
Schwarzenegger, who had attended at the request of a seventh-grader, talked to the group about the value of after-school programs. He left through a back exit without taking more questions from reporters.
Aides said Schwarzenegger will give more detailed program announcements and make more public appearances at a time of his choosing.
Shultz is currently a fellow at the Hoover Institution at Stanford University. He was secretary of state from 1982 to 1989 in the first Bush administration and previously served on President Reagan's Economic Policy Advisory Board. During the Nixon-Ford presidencies, he was Treasury secretary from 1972 until 1974 and secretary of labor from 1969 until 1970.