Mr Kerik, who was police commissioner at the time of the 9/11 attacks, had been due to stand trial next week.
He had his bail revoked two weeks ago for passing on secret pre-trial documents and has been in prison since.
He made false statements to the White House in 2004 while being considered for a job as homeland security chief.
Mr Kerik made his eight guilty pleas at a court in White Plains, New York state.
The admissions are part of a plea bargain designed to resolve three pending criminal trials on 15 federal counts. Mr Kerik had previously denied all charges.
He faces sentencing in February next year.
In court, Judge Stephen Robinson warned Mr Kerik that he could face up to 61 years in prison for the offences to which he was pleading guilty.
Under the plea bargain, the prosecution has suggested the former police commissioner be sentenced to between 27 and 33 months in jail.
Mr Kerik told the court he had given up his right to appeal. He has also agreed to file amended tax returns and pay restitution.
As well as making false statements to the White House and other federal officials, Mr Kerik admitted accepting a $250,000 (£151,000) payback in the form of apartment renovations from a company to which he gave a city contract.
He also admitted tax crimes including failing to report more than $500,000 (£302,000) in taxable income between 1999 and 2004.
Mr Kerik had been hailed as a national hero following the 9/11 terror attacks and was nominated for the post of the head of the Department of Homeland Security under the Bush administration in 2004.
But he withdrew his name from consideration for the role after he was accused of failing to pay taxes, and of having extramarital affairs.