The people spoke on condition of anonymity because the settlement hadn't been announced publicly, though that announcement was expected later Thursday.
One of the people, a law enforcement official familiar with the deal, said Transocean would pay $1 billion in civil penalties, $400 million in criminal penalties and would plead guilty to violating the Clean Water Act.
BP PLC, which leased the rig from Transocean, already has agreed to pay a record $4.5 billion in penalties and plead guilty to manslaughter and other criminal charges related to the spill. The deal with BP doesn't resolve the federal government's civil claims against the London-based oil company.
In September, Transocean said in a regulatory filing that it had discussed a $1.5 billion settlement with the Justice Department that had to clear several hurdles before it could be completed. The company said one sticking point was whether a settlement would include claims for environmental damage under the Oil Pollution Act of 1990.
Transocean previously announced it had reserved $2 billion for paying claims related to the Deepwater Horizon disaster.
Transocean also said in the September filing that it had rejected settlement offers last year from BP and a group of attorneys for Gulf Coast residents and businesses who blame the spill for economic damages. Those claims are still pending.
Last month, U.S. District Judge Carl Barbier in New Orleans gave final approval to a class-action settlement agreement between BP and a team of private plaintiffs' attorneys. BP estimates it will pay about $7.8 billion to resolve these claims, but the settlement isn't capped.
Barbier also is set to preside over a trial designed to identify the causes of BP's deadly well blowout and assign percentages of fault to the companies involved. The first phase of the trial is scheduled to start Feb. 25.
BP reported profits of more than $25 billion in 2011, but for Transocean the year resulted in a loss of about $5.7 billion, some of it attributed to contingencies for litigation resulting from the sinking of the Deepwater Horizon.
A series of government investigations has spread out the blame for the nation's worst offshore oil spill among BP, Transocean and other partners on the project, including cementing contractor Halliburton.
The Deepwater Horizon was drilling in water a mile deep about 50 miles southeast of the Louisiana coast when it exploded on the night of April 20, 2010.
The rig burned for about 36 hours before sinking.
As engineers made repeated attempts to halt the flow of oil from BP's busted Macondo well, millions of gallons of crude flowed out. Marshes, beaches and fishing grounds across the northern Gulf were fouled by the oil.