Softbank-owned Fortress, Canada Pension Plan Investment Board and Koch Real Estate Investments will pay 252p per share plus a 2p special dividend. The offer is subject to shareholder approval.
Andrew Higginson, chairman of Morrisons, said: "The Morrisons directors believe that the offer represents a fair and recommendable price for shareholders which recognises Morrisons' future prospects.
"Morrisons is an outstanding business and our performance through the pandemic has further improved our standing and enabled us to enter the discussions with Fortress from a hard-won position of strength.
"We have looked very carefully at Fortress' approach, their plans for the business and their overall suitability as an owner of a unique British food-maker and shopkeeper with over 110,000 colleagues and an important role in British food production and farming.
"It's clear to us that Fortress has a full understanding and appreciation of the fundamental character of Morrisons.
"This, together with the very clear intentions they have set out today, has given the Morrisons directors confidence that Fortress will support and accelerate our plans to develop and strengthen Morrisons further."
The deal comes after Morrisons rejected a takeover proposal from New York-based firm Clayton, Dubilier & Rice (CD&R) last month.
UK supermarkets have been buoyed by the pandemic with sales boosted by the closure of non-essential shops and hospitality firms.