Morrisons beat a rival offer from EG Group, the petrol station empire, owned by the billionaire Issa brothers.
It will pay off McColl's £170m debts and take on all 1,160 shops, including 17 in South Yorkshire, and pension schemes with 2,000 members.
The supermarket's boss said the deal offered stability and continuity for the business, staff and pensioners.
Morrisons is a wholesale supplier to McColl’s. It also has a deal to convert hundreds of McColl's shops to Morrisons Daily convenience stores.
McColl’s in Sheffield include Rural Lane, Wisewood; Ecclesall Road South, Hutcliffe Wood Road, Margetson Crescent, Low Edges Road and Green Lane, Dronfield.
It has stores in Rotherham at Whitehill Lane; St John’s Green and Oaks Lane, Kimberworth Park; Broom Valley Road, Kilnhurst Road, Fleming Way and Wales Road.
It also has Green Spring Avenue, Barnsley; Cuttholme Way, Loundsley Green, Chesterfield; Union Street, Harthill and Thomas Street, Swinton, Mexborough.