Lee is stepping down to become the chief executive of Rustan Supercenters Inc, a supermarket chain in the Philippines, his native country. He joined Morrisons in July last year to help turn the group around.
The former Proctor & Gamble boss is leaving Morrisons days after the company announced it would get a discount on its new warehouse deal with Ocado, boosting Morrisons' shares.
Morrisons is taking capacity in Ocado's new warehouse in Erith. Ocado will also develop "store pick" technology for Morrisons' website.
Andrew Higginson, Morrisons' chairman, said: "We are very sorry that Irwin is leaving us all with his enthusiasm and drive, and with his extensive supplier knowledge. However, we fully understand and respect Irwin's decision to move back into a full time executive role and to relocate.
"We wish him and his family all the very best for the future and thank him for his contribution."
Lee said he had enjoyed his time on the board at Morrisons, "contributing to the turnaround and growth strategy reset."
He added: "I have no doubt Morrisons will continue the improvement trend we've begun to see."