NEW ORLEANS — A federal judge has given final approval to BP’s settlement with a bulk of businesses and individuals who lost money because of the 2010 oil spill in the Gulf of Mexico.

BP PLC has estimated it will pay $7.8 billion to resolve economic and medical claims from more than 100,000 businesses and individuals hurt by the nation’s worst offshore oil spill. The settlement has no cap; the company could end up paying more or less.

U.S. District Judge Carl Barbier, who gave his preliminary approval in May, made it final in a 125-page ruling released Friday evening.

“None of the objections, whether filed on the objections docket or elsewhere, have shown the settlement to be anything other than fair, reasonable, and adequate,” he wrote.

After Barbier’s preliminary approval in May, thousands of people opted out of the settlement to pursue their cases individually. More than 1,700 changed their minds and asked to be added back in by a Dec. 15 deadline, Barbier said.

There is still a lot of litigation left, including a trial to identify the causes of BP’s blowout and assign percentages of fault to the companies involved, Barbier wrote. That trial is scheduled next year.