The Israeli has agreed a two-year contract, the Football Association of Zambia (FAZ) announced on Thursday.
"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, but resigned after finishing fourth in the same competition two years later.