His two-year contract with the Ghana Football Association was due to expire at the end of this month.
“After an extremely amicable meeting with the president of Ghana FA, and following more than two successful years in charge of the national team, I’ve informed Mr Nyantakyi that time is right for me to move on to a new challenge and I thank him for the opportunity,” Grant’s statement said.
“I’ve hugely enjoyed my time in Ghana taking over after the disastrous 2014 World Cup campaign and rebuilding the squad to reach the final in the African Cup of Nations for only the second time in 23 years, and also the semi final of this year’s competition.
“I’m proud of the fact that I’m leaving an extremely professional, strong squad of players of a good age, who I’m sure will go on to achieve great success in the future.
“The passion and loyalty of the supporters is something I’ll always remember.”
Grant, 62, was tasked by the Ghana Football Association to win the 2017 AFCON but he fell short at the semi-final stage after losing 2-0 to eventual winners Cameroon.
He placed fourth after losing 1-0 to Burkina Faso in the third place match.
When Grant was appointed in November 2014, Ghana was ranked 37th on the FIFA Coca Cola World rankings but he leaves with the Black Stars a lowly 54th as at January 2017.
He handled 29 matches during his tenure; winning 14, drawing 8 and losing 7 games.