The Black Stars saw their continental hopes come to an end at the semi-finals as they lost to eventual champions Cameroon, while Burkina Faso added insult to injury by beating the Ghanaians 1-0 in the third-place playoff.
Ghana FA officials revealed prior to their bronze medal defeat that former Chelsea coach Grant would not have his two-year contract extended, and that news has since been confirmed by the tactician.
"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 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."