Veteran politician Kembo Mohadi will be sworn in as the other vice-president.
The pair, who were appointed by President Mnangagwa, had been elevated to similar positions in the ruling Zanu-PF party on Saturday.
Chiwenga retired from the military this month. His appointment was expected as a reward for leading Mugabe’s overthrow.
This also adds to signs of a consolidation of power for the army since it turned against the 93-year-old Mugabe.
Mnangagwa has appointed several senior military officers to his cabinet and the ruling party’s top decision-making body, the politburo.
The president is under pressure from opposition parties and the public to implement political reforms.