The bank's civil and criminal settlements would also involve a deferred prosecution agreement, a criminal action that would suspend an indictment as long as the bank acknowledged the facts of the government's case and changed its behavior, the Times said.
JPMorgan (JPM) will pay more than $1 billion to the prosecutors in Manhattan and the remainder to the Office of the Comptroller of the Currency and a unit of the Treasury Department investigating breakdowns in the bank's safeguards against money laundering, according to details of the deal.
The government plans to use some of the payout for Madoff's victims, the newspaper said.
Madoff was convicted in 2009 of defrauding thousands of investors and is serving a 150-year prison sentence.
JPMorgan spokesman Joseph Evangelisti declined to comment on the New York Times report when contacted by Reuters.
Once reaching the Madoff settlements, the bank will have paid some $20 billion to resolve government investigations over the last 12 months, the newspaper said.
A government official told Reuters last month that the U.S. Treasury Department's Office of the Inspector General was examining whether JPMorgan interfered with the OCC's attempts to probe the bank's relationship with Madoff.
Madoff had also separately told U.S. authorities that JPMorgan -- the bank he had used during his decades-long investment scam -- had tried to stop the OCC from getting information about their relationship.