Botey's new position was announced on state television late on Tuesday. She is the first woman named Prime Minister in the West African state.
Obiang, 80, was re-elected for a sixth term in office in November with 95% of the vote, cementing his place as the world's longest-standing ruler.
The United States said at the time it had "serious doubts about the credibility of the announced results" in the election and called on authorities to work with all stakeholders to address allegations of voter fraud.
The country of around 1.5 million people has had only two presidents since independence from Spain in 1968. Obiang ousted his uncle, Francisco Macias Nguema, in a coup in August 1979.