Christie, 46, sent an e-mail to supporters, The Star-Ledger of Newark reported. He said he will make a formal announcement early next month.
In the e-mail, Christie said that New Jersey has government spending and taxes that are too high.
"New Jersey's taxes have become so unaffordable that more families are leaving our state than moving here," he wrote. "Our state's business tax climate is ranked 50th in the nation and has become so unattractive to employers that only government jobs are growing in New Jersey."
Christie, who pursued a number of high-profile corruption cases while he was U.S. attorney, has a far bigger reputation statewide than the other announced Republican candidates, state Assemblyman Rick Merkt and former Bogota Mayor Steve Lonegan.
Gov. Jon Corzine, who entered politics after serving as president of Goldman Sachs, has been struggling with major budget problems. His fellow Democrats refused to back a plan to reduce the state deficit by using dramatic toll increases on the New Jersey Turnpike and Garden State Parkway.
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