NEW ORLEANS — A federal judge on Tuesday approved an agreement for BP PLC to plead guilty to manslaughter and other charges and pay a record $4 billion in criminal penalties for the company’s role in the 2010 rig explosion and oil spill in the Gulf of Mexico.

U.S. District Judge Sarah Vance said the plea deal was “just punishment” considering the alternatives to the settlement, including the risk that a trial could result in a lower fine for BP.

Before she ruled, Vance heard emotional testimony from relatives of 11 workers who died when BP’s blown-out Macondo well triggered an explosion on the Deepwater Horizon drilling rig and started the spill.

BP agreed in November to plead guilty to charges involving the workers’ deaths and for lying to Congress about the size of the spill from its broken well, which spewed more than 200 million gallons of oil.

The deal doesn’t resolve the federal government’s civil claims against BP. The company could pay billions more in penalties for environmental damage.

BP separately agreed to a settlement with lawyers for Gulf Coast residents and businesses who claim the spill cost them money. BP estimates the deal with private attorneys will cost the company roughly $7.8 billion.

For the criminal settlement, BP agreed to pay nearly $1.3 billion in fines. The largest previous corporate criminal penalty assessed by the Justice Department was a $1.2 billion fine against drug maker Pfizer in 2009.

The criminal settlement also includes payments of nearly $2.4 billion to the National Fish and Wildlife Foundation and $350 million to the National Academy of Sciences.