Dr Tamakloe told the Ministry of Youth and Sport in a letter that the court's decision had effectively made his position untenable.
Dr Tamakloe is said to see himself as a reformer and his one-year term in office has been marked by spats with different parts of the football community in Ghana.
The executive council of the GFA began impeachment proceedings after Dr Tamakloe questioned their powers, size and essence in a private letter to the Ministry of Sport.
He said it was "absurd" that the GFA's statutes give control of football matters to the executive council while the management board are put in charge of administration.
"The GFA has an unwieldy body of 37 members superintending the day-to-day activities of a five-member board which makes neither common nor business sense," he charged.
World football governing body FIFA has long called for reforms of the GFA's statutes.
