Supervalu Inc. is selling five of its top supermarket chains — Albertsons, Acme, Jewel-Osco, Shaw’s and Star Market — to an investor group owned by Cerberus Capital Management for $100 million in cash.

Cerberus’ AB Acquisition group will also acquire $3.2 billion in debt in taking over the 877 stores.

In addition, the investor group said it will try to take between a 19.9% and 30% stake in Supervalu. The tender offer of $4 a share represents a nearly 32% premium on Supervalu’s closing price Wednesday.

Eden Prairie, Minn.-based Supervalu will be left with its wholesaling business, 1,300 Save-A-Lot discount grocery stores and regional chains Cub, Farm Fresh, Shoppers, Shop ‘n Save and Hornbacher’s.

Quiz: How well do you remember 2012?

Supervalu stock was up as much as 19% Thursday, reaching $3.62 a share.

Sam Duncan, a longtime grocery industry veteran, will replace Wayne Sales as Supervalu’s president and chief executive once the acquisition closes. The Supervalu board will shrink from 10 members to seven once the deal goes through, with five current directors set to resign and a Cerberus-led investor consortium poised to choose two others.

After a longer search process, the board will expand to include 11 directors total.

Supervalu said it plans to “focus on right-sizing operations and maximizing efficiencies” going forward, generating annual revenues of more than $17 billion. The company said it has 125,000 employees.

In September, Supervalu said it would close 26 Albertsons stores by the end of 2012, including 18 in Southern California. Among all its chains, Supervalu said it would shut 60 stores nationwide.

New York-based private equity firm Cerberus said last month that it was selling Freedom Group, which produces the Bushmaster line of firearms. Adam Lanza is believed to have used one of the weapons in his assault on Sandy Hook Elementary School in Connecticut.