It will pay off McColl's £170m debts and take on all 1,160 shops, including those in Worksop, Retford and Blyth.
The supermarket's boss said the deal offered stability and continuity for the business, staff and pensioners.
The business’ collapse on Friday had sparked fears for the future of local jobs .
But PwC, joint administrators, confirmed it had been bought by Alliance Property Holdings Limited, part of the Morrisons Group, the group's largest supplier.
It said the deal successfully transferred all employees and shops, and included agreement to rescue the group's two pension schemes with more than 2,000 members.