The stock market’s Takeover Panel said Fortress offered 286p per Morrisons ordinary share, while CD&R offered 287p – meaning its bid amounts to an offer of almost £7 billion.
The final offer for the supermarket will now be voted on by shareholders on October 19.
Andrew Higginson, chairman of Morrisons, said the offer "represents excellent value for shareholders, while at the same time protecting the fundamental character of Morrisons for all stakeholders."
How will the bid affect shoppers and workers?
CD&R and Morrisons have been keen to stress they want to uphold the supermarket’s values and have attempted to ward off suggestions they will start selling off vast swathes of the company’s freeholds.
Supermarkets typically lease properties, whilst Morrisons continues to own around 90% of its estate.
How did CD&R win the battle?
The takeover saga has dragged on since CD&R first made an approach for the Bradford-based grocer back in June, leading to speculation the sector was ripe for private equity takeovers.
Following the initial bid, rival Softbank-backed Fortress made an offer of £6.3 billion in July.
But shareholders felt this was too low and Fortress, which owns Majestic Wines, returned with an increased offer of £6.7 billion in August, which the board accepted.
Later that month CD&R, which boasts former Tesco boss Sir Terry Leahy as an adviser, returned with an increased bid of £7 billion.
This led to the board withdrawing its support for the Fortress bid and throwing its weight behind the higher offer.
But because neither side made a formal bid, the Takeover Panel launched an auction process.
Both sides agreed beforehand that all bids would be at a fixed cash price and could not include stakes in other businesses or dividends to shareholders.
On Saturday, Sir Terry said CD&R was "gratified by the recommendation of the Morrisons’ board."
What has been the reaction to the takeover?
Seema Malhotra, shadow minister for business and consumers, said: “The new owners must urgently deliver binding assurances for workers, pension fund holders, and local people. “Government has a responsibility too. It must ensure that the new owners are responsible, long-term investors, seeking to build the business for the future, and that decisions taken are also in the public interest. “We cannot see a repetition of previous cases where businesses have been loaded with debt and asset-stripped. Morrisons is a great British company which must be safeguarded for the future.” Joanne McGuinness, Usdaw national officer, said: “Now that the future ownership of Morrisons seems clearer we are seeking discussions with the prospective new owners, to ensure that our members’ interests and the long-term future of the business are protected throughout this process. “Our main concerns are about job security, while maintaining and improving our members’ terms and conditions of employment. “We have heard the assurances already given and welcome the constructive working relationship that Usdaw has experienced so far.”
There have been concerns that any new owner may reduce the supermarket’s tax bill, with off-shore shell companies set up ahead of the takeover.
Morrisons’ pension trustees will have to be consulted, although earlier this month they said an agreement had been reached with CD&R.