Bah Ndaw, a former defence minister, was picked by the coup leader, Colonel Assimi Goita, to head a transitional government until elections are held.
Col Goita will be his vice-president.
The new government is expected to be in office for a transition period of 18 months that will lead to an election.
The appointment of a civilian president was a condition for the West African regional group, Ecowas, to lift the sanctions it imposed after the coup.
Stocks of goods are running low in the capital, Bamako, where businesses are hoping for an announcement from Ecowas after the inauguration.