The deal has been unanimously accepted by the board of the grocery chain and directors have said shareholders should vote in favour of the takeover at a meeting due in early October.
It means the company has withdrawn its recommendation for investors to accept a previous £6.7bn takeover deal from a consortium led by rival private equity firm Fortress, which released a statement saying that it was “considering its options”.
Last week, CD&R was given an extended deadline until Friday afternoon by takeover regulators to say whether it wanted to make a new offer for Morrisons, or walk away.
CD&R had originally been turned down by the Morrisons board over a potential £5.5bn bid.
In June, the board said the offer "significantly undervalued Morrisons and its future prospects".
Since then CD&R has been pondering whether it should increase its bid for the chain.
In the updated offer document, released late on Thursday night, the company said it "recognises the legacy of Sir Ken Morrison, Morrisons' history and culture, and considers that this strong heritage is core to Morrisons and its approach to grocery retailing".
The private equity house said it "will support Morrisons in further building on these strengths" and suggested it had no plans to sell off its freehold stores.
Danni Hewson, AJ Bell financial analyst, said: “Will Fortress pick itself off the mat and find another level? It is a real possibility.”