Politicians, army officers and diplomats applauded Henrique Rosa after he took office in a ceremony at a hotel in capital Bissau.
Antonio Artur Sanha was sworn in as the new prime minister on the occasion.
"Being chosen gives me honour, but also responsibility. My position demands prudence and modesty, because the challenges are enormous," Rosa said after taking oath.
Rosa and Sanha were nominated by the military junta, that seized power in the country of 1.3 million on 14 September.
Rosa's predecessor, Kumba Yalla had failed to resolve the country's economic woes and was deposed.
A former Portuguese colony, Guinea-Bissau is among the world's poorest countries. The annual average income is a paltry $170 dollars.
Under a transition pact signed by the army and political parties earlier on the day, parliamentary elections will be held within six months followed by presidential polls to elect Rosa's successor an year later.
"The transition period will not be at all easy," coup leader General Verissimo Correia Seabra said, after swearing in Rosa.
The general is to head the National Transition Council to supervise Rosa and the electoral committee until a parliament is elected.