He has been criticized for his $600,000-plus salary package, which included a $250,000 annual salary and $11,500 living allowance. The package was approved by church members.
Dissidents unsuccessfully tried to block his installation by going to court. They charged the package strained the church's budget.
The cathedral on Manhattan's Upper West Side was built by John D. Rockefeller.
A church spokeswoman says Braxton's "end date will be determined after further discussion with church leadership."
The New York Times first reported the story on its Web site Tuesday.
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