Stevanovic was dismissed after failing to guide the Black Stars to the Africa Cup of Nations final, with Appiah put in temporary charge.
Now Appiah, who has been assistant coach of the national team since 2008, has been given the main job on a permanent basis.
"The Ghana Football Association has appointed James Kwesi Appiah as the substantive head coach of the Black Stars," read a statement from the Ghana FA.
"The meeting was called to discuss the head-hunting exercise undertaken by the GFA to find a permanent Black Stars coach."
Ghana finished fourth in this year's Africa Cup of Nations, losing to eventual winners Zambia in the semi-final before going down to Mali in the third-place play-off.