Morrisons also said it will take over the company’s two pension schemes.
McColl's fell into administration on Friday, plunging the future of its shops and staff into doubt.
The UK’s fourth-largest supermarket chain and forecourt giant EG Group both tabled final offers on Sunday to secure a rescue deal.
EG – whose owners also run supermarket giant Asda – had initially been favourites to complete a rescue deal for McColl’s.
Morrisons’ early approach had reportedly been rejected by lenders who preferred EG’s offer to instantly repay more than £160 million ($198m) in debt from McColl’s.
But it is understood that Morrisons’ successful move will also repay the lenders in cash.
In a statement after the deal was announced, Morrisons said “the secured lenders and preferential creditors will be paid in full with a distribution also expected to unsecured creditors”.
Morrisons had originally proposed to save the “vast majority” of jobs and shops but improved this offer during the bidding process.
“All McColl’s colleagues will be transferred with the McColl’s business to Morrisons,” the supermarket said on Monday.
Morrisons chief executive David Potts said: “Although we are disappointed that the business was put into administration, we believe this is a good outcome for McColl’s and all its stakeholders. This transaction offers stability and continuity for the McColl’s business and, in particular, a better outcome for its colleagues and pensioners.
“We all look forward to welcoming many new colleagues into the Morrisons business and to building on the proven strength of the Morrisons Daily format.”
A representative of McColl’s Pension Schemes said: “The trustees welcome the announcement that Morrisons will continue to support the schemes following its acquisition of the McColl’s business.
“The trustees will continue to engage with all stakeholders to ensure that members’ benefits are protected following the completion of the transaction.”
McColl’s filed a notice to appoint administrators from PwC on Friday and formally entered administration on Monday.
Morrisons is currently McColl’s wholesale supply partner and was expected to immediately terminate its deal with the convenience chain if the takeover bid proved unsuccessful.
McColl’s also runs about 270 stores under the Morrisons Daily brand.
It is understood that administrators were favourable to deal with Morrisons because the Bradford-based supermarket was one of McColl’s biggest creditors.
The deal comes less than a year after Morrisons itself was bought for £7 billion ($8.64bn) by US private equity company Clayton, Dubilier & Rice (CD&R).
McColl’s collapse has come after a financial struggle over the past two years as it witnessed soaring costs due to supply chain disruption, inflation and its large debt burden.
“Morrisons already has a wholesale supply agreement with McColl’s, so this may have aided negotiations with the administrators and helped to speed up decision-making on both sides," said Simon Underwood, business recovery partner at accountancy firm Menzies LLP.
“The speed of this deal will come as a great relief to employees, lenders and all creditors with a vested interest in the convenience store chain.”