The move comes after private equity firm Cerberus bought 80.1% of Chrysler for 7.4bn euros ($10.1bn; Ј5bn) from parent company Daimler.
Last month, the former boss of DIY store Home Depot, Bob Nardelli, was named Chrysler's president.
"We're thrilled that one of the most successful executives in the history of the auto industry has joined our leadership team at the new Chrysler," Mr Nardelli said.
Wider reorganisation
Mr Press was president of Toyota's North American operations and senior managing director at the Japanese carmaker.
As head of Toyota Motor Sales, he helped the firm boost sales from a 9.3% market share in 2000 to 13.1% in 2003.
"Jim has played a significant role in strengthening Toyota's presence in the US," said Toyota's president Kasugai Watanabe.
Chrysler - like other US car firms - has faced increasingly tough competition from Japanese companies that have developed smaller, more fuel efficient models.
The appointment of Mr Press and other executives comes as part of a wider reorganisation plan that is set to reduce the workforce by 13,000 in the US and Canada by 2009.
Chrysler is currently in talks with the United Auto Workers Union (UAW) over pay and benefits for its staff.