A statement issued by the presidency said the cabinet has also stepped down under provisions of the west African country’s constitution.
It went on say the government would continue to run affairs until a new one was appointed.
According to analysts in the capital, Ouagadougou, Mr Yonli is likely to be reappointed to the new government that could possibly be announced in the next few days.
President Compaore, 54, rose to power in a coup in 1987 but would later allow elections, all of which he would go on to win.
He was recently reelected in November claiming more than 80 percent of the vote.
It was the first election where Mr Compaore had faced committed but fractured opposition, beating 11 separate candidates.
His opponents again alleged this ballot was an "electoral masquerade" but decided there was no point in challenging the outcome.
The nation of Burkina Faso is landlocked between the Sahara desert and the coastal countries Ivory Coast and Ghana.
It is among the world’s poorest nations, with high unemployment and illiteracy.