The entire offer is worth £9.8bn, including net debt, constituting 287p per share. It beat rival bidder Fortress Investment Group's final bid to the punch by 1p per share.
The retailer’s board has unanimously approved the offer, which still needs to be ratified by Morrisons shareholders at a meeting on 19 October.
A bidding war for Morrisons began when its board announced on 3 July it was supporting a bid worth £6.3bn (254p per share) - or £9.5bn including payment of net debt - by a Fortress-led consortium.
Shareholder rejects Fortress' original offer
Morrisons largest shareholder then rejected Fortress' original offer and CD&R made a rival bid worth 230p per share. Fortress upped its offer to £6.7bn excluding debt, which was in turn countered by a £7bn offer by CD&R.
There followed a hiatus while bidders attempted to convince Morrisons' pension scheme trustees they could guarantee future pension provision.
The situation moved to a duel between Fortress and CD&R in the form of the auction after neither side offered a final bid.
“Today's final offer from CD&R represents excellent value for shareholders while at the same time protecting the fundamental character of Morrisons for all stakeholders," Andrew Higginson, chair of Morrisons, said.
"CD&R have good retail experience, a strong record of developing and growing the businesses in which they invest, and they share our vision and ambition for Morrisons. We remain confident that CD&R will be a responsible, thoughtful and careful owner of an important British grocery business.
"Shareholders will now have the final say and, if the offer is approved, the board is confident that Morrisons will continue to go from strength to strength under CD&R's ownership.”
Leahy: 'excellent business'
Commenting on CD&R's final offer, Leahy said: “We are gratified by the recommendation of the Morrisons board and look forward to the shareholder vote to approve the transaction. We continue to believe that Morrisons is an excellent business, with a strong management team, a clear strategy, and good prospects.”
CD&R has said it still reserves the right to increase the amount of the offer price if a third party announces a firm intention to make an offer for Morrisons on or after the date of this announcement.