By Daniel Gilbert And Sarah Kent 

BP PLC agreed to pay $18.7 billion to settle all federal and state claims arising from the 2010 Deepwater Horizon oil spill, including the biggest pollution penalty in U.S. history.

If approved by a federal judge, Thursday's deal would conclude a monumental legal showdown over the Deepwater Horizon disaster, which killed 11 crew members aboard the drilling rig and caused the largest oil spill in U.S. waters.

The agreement would avert years of litigation over the environmental impact of a spill that leaked millions of barrels of crude into the Gulf of Mexico over the course of 87 days and coated hundreds of miles of sensitive beaches, marshes and mangroves with oil.

The settlement would add at least $10 billion to the roughly $44 billion BP has already incurred in legal and cleanup costs, pushing its tab for the spill higher than all the profits it has earned since 2012.

The company will pay far less in fines--$5.5 billion of the settlement's total--than the maximum $13.7 billion it faced under the federal Clean Water Act. But its payment would be the largest ever under that law, the government said, and the entire deal would be biggest it ever reached with a corporation.

The company previously struck a $4 billion deal to settle a federal criminal probe stemming from the disaster. The Deepwater Horizon exploded on the evening of April 20, 2010, after gas seeped into the well the rig was drilling, rocketed upward and ignited on deck. Survivors compared the blast to a freight train smashing into the vessel.

The rig soon sank. Plugging the leak took months while Americans watched live video of the flowing oil via an underwater "spillcam."

Investors eager for an end to the saga and five years of litigation celebrated the deal, sending BP's shares up 5.1% in U.S. trading on Thursday and adding more than $5 billion to its stock-market value.

BP's payments would be stretched out over 18 years at around $1.1 billion annually, softening the blow to the company's cash flow. The company expects to deduct much of the payouts from its taxes. And Fitch Ratings said the deal would strengthen BP's credit, helping it improve its balance sheet and cope with the yearlong downturn in oil prices.

BP Chairman Carl-Henric Svanberg said the agreement provides "a path to closure for BP and the Gulf."

"It resolves the company's largest remaining legal exposures, provides clarity on costs and creates certainty of payment for all parties involved," he said.

Most of the money will end up in the hands of Louisiana, Mississippi, Alabama, Texas and Florida to use for environmental remediation and economic development.

While state officials touted the benefits of the settlement, not all were pleased with every aspect of the deal.

U.S. Rep. Garret Graves, a Louisiana Republican, said the lengthy, multiyear payment period was overly generous to BP and called for a faster collection. Still, he said that Louisiana, the largest beneficiary among the states, got the $6.8 billion it was seeking.

Rep. Graves, formerly a top aide in the Louisiana governor's office, had been involved in 2013 settlement talks with BP that failed to reach a deal. A federal judge's rulings in the past year helped create momentum for a settlement, he said, adding, "These court decisions further tightened the noose around BP's neck."

U.S. District Court Judge Carl Barbier ruled last September that BP acted recklessly in disregarding warning signs that the well wasn't properly sealed against gas leaks, subjecting the company to the maximum fine under the Clean Water Act. In January, the judge determined BP was liable for spilling 3.19 million barrels of crude into the Gulf. Prosecutors sought at least $12 billion in fines under the act.

BP appealed those findings, but continued to suffer defeats in court. The U.S. Supreme Court earlier this week declined to hear an appeal that the company shouldn't have to pay civil pollution penalties for the spill. Judge Barbier was expected to rule soon on BP's Clean Water Act fine.

The company had been negotiating with the states and the U.S. Justice Department since the beginning of May under the supervision of Judge Barbier in New Orleans, according to a person familiar with the matter. The judge must approve the deal, which is also subject to a period of public comment.

In addition to the $5.5 billion in penalties under the Clean Water Act--$2 billion more than the company had set aside for that purpose--BP agreed to pay $7.1 billion to the U.S. and Gulf Coast states to cover long-term environmental damages that are still being assessed. It would also set aside $232 million for damages that aren't yet known, and would pay $5.9 billion to resolve economic and other claims made by the five states and more than 400 local governments.

U.S. Attorney General Loretta Lynch said the payment "would justly and comprehensively address outstanding federal and state claims, including Clean Water Act civil penalties and natural resource damages."

BP's lawyers had argued the company should pay no more than $2 billion under the Clean Water Act, offering evidence that its massive cleanup effort helped avert an environmental calamity and diminished its ability to pay a big fine. The company had rejected claims from state and local governments that sought a combined $35 billion in economic loss and property damage.

While the proposed settlement would resolve some of BP's biggest liabilities, the litigation over the spill isn't entirely over. The company faces about 3,000 civil cases in U.S. and foreign courts, which include lawsuits brought by shareholders, and has yet to set aside money for those potential costs.

BP's expenses from a 2012 civil settlement with Gulf Coast residents and businesses have continued to rise. The company's latest estimate is that it will pay $10.3 billion, up from an initial estimate of $7.8 billion. The deadline for filing claims was June 8.

"Everyone is getting a significant amount of money," Tom Claps, a litigation analyst at Susquehanna Financial Group, said of the settlement. "But BP gets to pretty much walk away and close this chapter."

Justin Scheck and Devlin Barrett contributed to this article.

Write to Daniel Gilbert at daniel.gilbert@wsj.com and Sarah Kent at sarah.kent@wsj.com

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