By Liz Hoffman

Updated June 2, 2015 6:02 p.m. ET

Safeway Inc. will pay a group of investment funds about 26% more than other shareholders received when the grocery chain was sold to private-equity-backed Albertsons earlier this year for $7.6 billion, a big win for hedge funds that challenge deals in court.

Albertsons will pay three funds, which owned about 6% of Safeway stock, $44 a share in cash, or about $127 million more, as part of a court settlement in a buyout-related lawsuit, according to people familiar with the matter. Other shareholders received $34.92 a share when the deal closed in January. Both groups of investors are still entitled to a portion of any proceeds Safeway might get from a sale of its stake in a Mexican joint venture.

The settlement comes in an appraisal lawsuit stemming from Safeway’s sale to Albertsons, which is owned by private-equity firm Cerberus Capital Management LP. In appraisal cases, investors—many of which are hedge funds that buy their shares on the eve of a takeover—oppose the deal and then sue for a higher price.

Appraisal cases have risen sharply over the past two years, particularly among hedge funds looking for ways to profit from an uptick in corporate mergers. Results have been mixed. Three recent court rulings awarded appraisal-seekers exactly the merger price, rather than the bump they were seeking. Funds can still profit, thanks to accumulated interest on their claims of around 5.75%, but many have promised their own investors double-digit returns, according to market participants.

Other large cases are pending over the buyouts of retailer PetSmart Inc., fruit grower Dole Food Co. and jewelry chain Zale Corp.

Safeway’s agreement resolves claims brought by investors owned 14 million shares, the bulk of the 17.7 million shares that had sought appraisal. The settling investors are Merion Capital LP, a Magnetar Financial LLC-backed vehicle and a Dutch pension fund, according to people familiar with the matter and a court filing, which didn’t disclose the financial terms of the agreement.

Two other hedge funds, Brigade Capital Management LP and Muirfield Capital Management LLC, didn’t settle and still own rights to about 3.7 million Safeway shares, filings show. Their cases are ongoing.

The settlement also doesn’t resolve lawsuits over whether Safeway’s board fulfilled its obligation to get investors the highest price possible. Such claims are typically litigated separately from appraisals, and any payouts they generate would be shared with all Safeway shareholders.

Albertsons and Cerberus agreed in March 2014 to buy Safeway for $32.50 in cash plus contingent consideration tied to the potential sale of Safeway’s joint ventures and real estate arms. Some of that has already been paid out to investors, who pocketed $34.92 when the deal closed.

Corrections & Amplifications

Albertsons will pay a group of investment funds $44 per share as part of a settlement of litigation over the company’s buyout, or about $127 million more than they would have received in the deal. An earlier version of this story had the incorrect price-per-share.

Write to Liz Hoffman at liz.hoffman@wsj.com