The job cuts represent about 5% of the bank's workforce, Bloomberg News said. The measures should save the company as much as $625 million a year by the end of 2014.
State Street said it will book before-tax restructuring expenses worth as much as $450 million over the next four years.
State Street CEO Joseph Hooley has set a long-term goal of boosting earnings by 10% to 15% a year. The company cut 1,700 jobs in the first quarter of 2009. It also reduced bonuses and the quarterly dividend.
The Federal Reserve has kept interest rates at nearly zero since Dec. 2008, when the financial crisis rocked markets.