Thieba, who has little political experience, is charged with forming President Roch Marc Kabore's government as the country continues with a democratic transition after 27 years under leader Blaise Compaore, who was overthrown in October 2014.
Thieba, 56, worked for many years as an economist for the West African central bank, BCEAO, in Ivory Coast.
Landlocked Burkina Faso produces cotton and gold but remains impoverished. Its economy has slowed due to lower global commodity prices and reduced investment during the democratic transition that began after Compaore fell.
Kabore has said the government needs to improve access to water, healthcare and education, according to Reuters.
It must also make sensitive political decisions after authorities under the interim government charged a prominent general with the murder of a previous president and issued an international arrest warrant for Compaore who fled after being toppled from power.