By Becky Yerak

Consumer-focused investment firm Capitol Peak Partners LLC and KKR & Co. won a bankruptcy auction for Borden Dairy Co., the milk producer known for its "spokes-cow" Elsie, people familiar with the matter said.

A joint venture between Capitol Peak and KKR was named the winning bidder after an auction to sell Borden's assets out of bankruptcy, according to the people and to court documents. Capitol Peak is led by Gregg Engles, a former chairman and chief executive of Dean Foods Co., a longtime rival to Borden.

Capitol Peak, founded in 2017, is the senior partner in the joint venture, while KKR is the junior partner, a person familiar with the matter said.

KKR is a major lender to Borden, which filed for bankruptcy in January amid falling milk consumption in the U.S., rising freight costs and the growing clout of retailers consolidating with other merchants or beginning to develop their own milk-processing operations.

Any sale requires approval from the U.S. Bankruptcy Court in Wilmington, Del. A hearing on the sale is scheduled for Thursday.

Borden tried unsuccessfully to merge with Dean in April, before Dean's assets were purchased out of bankruptcy by Dairy Farmers of America Inc., the nation's largest dairy cooperative by membership.

The proposed deal would mark KKR's return to the ranks of Borden owners. In 1995, KKR bought Borden for $2 billion and took it private. Over the next decade, Borden underwent a series of reorganizations, which ultimately resulted in KKR selling off many Borden brands.

When Borden filed for bankruptcy, it had about $250 million in secured debt, including a $175 million term loan held by lenders including KKR. The investment firm used what it was owed on the loan as currency toward the bid for Borden, people familiar with the matter said.

Heading into bankruptcy, Borden's owners included private-equity firm Acon Investments LLC. Borden Chief Executive Tony Sarsam told The Wall Street Journal shortly after the bankruptcy filing that he believed Acon would remain the primary owner of the business after the bankruptcy.

Borden named Prairie Farms Dairy Inc. as a backup bidder behind the Capitol Peak-KKR venture, according to court records.

Write to Becky Yerak at becky.yerak@wsj.com