The in-form Al Sadd star left Qatar after Friday's 4-0 thrashing of Al Arabi.
Ayew scored the fourth goal of the game to make it four goals in four straight matches.
He will be meeting new coach Milovan Rajevac as the rest of the team start arriving this week.
The Black Stars will host Zimbabwe on Saturday, October 9, 2021, at the Cape Coast Stadium before travelling to Harare three days later for the second leg.
Ghana currently lies second on the table after a win and a defeat in the opening two matches of the qualifier.
Defeat to South Africa led to the sacking of coach Charles Kwablan Akonnor with the Serbian gaffer replacing him.
Milovan Rajevac has named a 32-man provision squad for the doubleheader. Read Full Story
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