Edinburgh-born Mr Sutherland, 43, has been recruited from retailer Kingfisher, owner of do-it-yourself chain B&Q in the UK, to succeed Peter Marks who is retiring.
He was raised in North Berwick and Bearsden, Glasgow, and worked at retailer Alliance Boots and soft drinks giant Coca-Cola before joining Kingfisher where he is chief operating officer.
But he has had links with Co-operative since 2010 when he became a non-executive director of its food business.
Mr Sutherland, 43, who is also a non-executive director of clothing retailer SuperGroup, will join Manchester-based Co-operative in May, but will continue working at Kingfisher until March.
He said: "The Co-operative is a great brand and I am very pleased to be given the opportunity to lead the organisation at this important time.
"The challenge is to build upon the success that has been achieved in recent years and the solid foundations that have been laid for its future growth."
Before taking on his current post, Mr Sutherland was chairman of B&Q and chief executive of Kingfisher UK & Ireland.
Co-operative chairman Len Wardle said: "I am delighted that Euan is to be the Co-operative Group's next group chief executive. He brings with him considerable experience of the strategic leadership needed in complex customer-facing businesses, across a variety of retail sectors, and we very much look forward to welcoming him and working together."
Co-operative did not disclose the pay package they have agreed with Mr Sutherland.
However, Mr Marks received nearly £1.7m in pay and benefits in 2011, down from £2.1m the year before.
Co-operative's £750 million acquisition of Lloyds's Verde portfolio is due to complete by November next year.
Integration of the business is expected to take another three to five years.
The deal will hand Co-operative 189 bank branches in Scotland, on top of the four it currently operates under the Co-operative Bank and Britannia brands.
As a result many observers had expected Co-operative to recruit a chief executive with financial services experience.
Instead, they have gone for someone with a background in retail. And there are signs that its food business, in particular former Somerfield stores, need some attention.
The Co-operative Group's core food division reported falling sales in the first half of the year, although its convenience stores have done better.
Co-operative is the fourth-largest food retailer in Scotland, and the group employs 11,000 people north of the Border.
The mutual, which has 475,000 Co-operative Group members in Scotland, has continued to grow its presence, acquiring the 28-strong David Sands chain this year. The stores will be reopened as Co-operative Foodstores. It also has 120 funeral homes, 60 pharmacies, a new £35m regional distribution centre at Newhouse, near Glasgow, three farms and two packhouses.
Mr Sutherland had been seen by some in the City as potentially an heir to Kingfisher's current chief executive Ian Cheshire. Seymour Pierce analyst Freddie George said: "(Sutherland) was, in our view, a major contributory factor in the recovery of the UK business over the past five years.
"As a result of the weakening trend, we believe management will be under pressure to consider a share buyback or special dividend."
UK sales at Kingfisher were hit by extremely wet summer weather in 2012, while the decline in the euro has depressed profits in France, its largest market.
In November, the company said uncertainty over Government Budget plans had knocked quarterly profits at its French operations down 6%.
Kingfisher shares were little affected by the news of Mr Sutherland's exit, rising 1.5p to 278.5p.