Grant took over from Kwesi Appiah in December 2014 and guided the national side to a second-place finish at the 2015 Afcon in Equatorial Guinea.
However, he was unable to repeat that feat this time around, losing 2-0 in the semi-finals to eventual winners Cameroon and also falling to a 1-0 defeat against Burkina Faso in the third-place playoff.
"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," the 61-year-old told Sky Sports.
"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 Africa Cup of Nations for only the second time in 23 years, and also the semi final of this year's competition."
He added: "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."
During Grant's 26 months in charge of Ghana, he played a total of 29 games and won 14, with eight draws and seven defeats. He recorded a winning rate of 48 per cent, as well as 1.4 goals scored per game and 0.7 goals conceded per game.
Goal understands that the search for his successor has begun, ahead of the Black Stars' World Cup qualifier against Congo in August.