The former Chelsea, West Ham and Ghana manager is now to take charge of Zambia after he signed a two-year contract with the African side.
The Football Association of Zambia (FAZ) announced the appointment on Thursday.
The 67-year-old, who has won honours as a manager in his home country, as well as in England and Serbia, replaces former Zambia international Moses Sichone who had been acting as caretaker.
“I was looking for the right challenge and that’s why I chose Zambia,” Grant said at a press conference in Lusaka.
“I came here because of the challenge and I hope when I leave here I will look around and say we did a good job and made a good foundation for the future.
“I think Zambia has the potential, we have set the targets of what we want to achieve.”
Grant has previous experience managing in Africa, having led Ghana to the final at the 2015 Africa Cup of Nations, where they were beaten on penalties by Ivory Coast.
Grant’s first game in charge of Zambia will be at home to Lesotho in March, a qualifier for the 2023 Cup of Nations being held in Ivory Coast.