NEW YORK—A judge on Monday approved a settlement in the long-running legal fight between Lehman Brothers Inc. and Barclays PLC, punctuating one of the more intriguing sagas of Lehman's collapse and its aftermath.

Judge Shelley C. Chapman of U.S. Bankruptcy Court in Manhattan said the deal, which calls for Lehman to pay Barclays $1.28 billion for so-called margin assets tied to Barclays's purchase of Lehman's brokerage business in 2008, was "fair and equitable."

"The settlement agreement as a whole is in the paramount interest of the creditors," Judge Chapman said. The settlement was announced earlier this month.

The legal battle over the assets, which climaxed in a 34-day trial back in 2010, ends with both sides agreeing to drop all litigation against the other.

More than $580 million cash will become available for Lehman creditors, because Lehman had set aside about $1.87 billion for the dispute. Both Barclays and James W. Giddens, the trustee unwinding Lehman's brokerage, have said the payment is about $80 million less than Mr. Giddens would have had to pay without a settlement.

Hughes Hubbard & Reed LLP's Sam McCoubrey, a lawyer for Mr. Giddens, said that while he would have preferred to prevail in court, the settlement was best "based on where we are today."

"We are pleased the Court approved this agreement, as it ends years of litigation and achieves the best result under the circumstances," Mr. Giddens said. "Winding-down and closing the estate continues in earnest, and we will continue efforts to appropriately distribute available assets from the general estate."

When the deal was announced earlier this month, Barclays said it expects the settlement to fetch it a pretax gain of about $750 million in its 2015 interim results, which will be announced July 29.

The fight over the sale to Barclays began in 2009, when the Lehman brokerage and its parent company both sued Barclays, saying the British bank negotiated a secret discount when it bought Lehman's brokerage.

The dispute came down to a "clarification letter" that was agreed on by the two sides in the hectic days of September 2008 but never was reviewed by James Peck, the judge who was then overseeing Lehman's bankruptcy case. The judge ultimately decided, while he didn't approve the terms of the letter explicitly, all parties involved treated it as if he had. The letter spelled out the terms of which assets would go to Barclays and which would stay with Lehman.

While Judge Peck had said in court that "no cash" could be transferred from Lehman to Barclays, some assets that the trustee later construed as cash did end up being transferred, per the letter. After the trial, the judge ultimately concluded that Barclays didn't receive an improper "windfall" from the sale but that Lehman's brokerage was entitled to the approximately $4 billion in money described as margin assets.

Later, however, a three-judge court of appeals panel said "ambiguities and loose ends were inevitable" in such a speedy sale and ruled that Barclays was entitled to these disputed assets. Lehman appealed to the U.S. Supreme Court, which declined to hear the case.

Lehman collapsed into the biggest bankruptcy in history in 2008. Since then, the investment bank and its brokerage have sorted out claims and reached settlements in an effort to pay back creditors as much as possible.

While individual customers of the U.S. brokerage received about $92.3 billion almost immediately after Lehman collapsed, other brokerage creditors had to wait until all others with "customer" status got 100% of their money back. Since July 2014, $5.9 billion has been distributed to unsecured creditors, meaning Mr. Giddens has returned about $112 billion in all to customers and creditors of the brokerage.

Creditors of Lehman's parent company have received more than $100 billion, a figure that includes claims between Lehman affiliates.

Write to Joseph Checkler at joseph.checkler@wsj.com

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