Thieba, 55, a former central banker, who is little known to the public, now will form a government.
His nomination follows the swearing in last week of Kabore, Burkina Faso's first new leader in almost three decades who has pledged to "reform institutions and modernise the government, for more social justice, democracy and freedom."
Kabore takes over from an interim administration that followed a popular insurrection in October 2014 that toppled Blaise Compaore, who had been in power since 1987.
The new premier has also held several posts in the Central Bank of West African States.
Kabore, who was elected with more than 53 per cent of the votes in a presidential poll late November, also has an economic background, but turned in the 1990s from a banking career to politics.
In January 2014, he went into outspoken opposition against Compaore and played a role in the "Citizen's Broom" movement that brought down the regime, to become the first democratically elected civilian leader of the country.
Kabore has pledged to build "a new Burkina Faso" by fighting youth unemployment, improving education and modernising the health system in the country of 17.4 million.
More than 46 per cent of Burkinabe people live below the poverty threshold.
