Modibo Keita, no relation to the President, was Prime Minister for three months in 2002 under then-President Alpha Oumar Konare. Last year, he headed the government delegation in negotiations with separatists from the north of the country, which took place in Algeria.
Islamists linked to Al Qaeda seized northern Mali in 2012, forcing a French-led military intervention in 2013 that scattered the fighters across a vast region with porous borders. The insurgents continue to carry out attacks.
"The president of the republic, in accordance with the constitution, decrees that Modibo Keita is Prime Minister," said the statement.
The previous Prime Minister, Moussa Mara, and his government resigned earlier on Thursday.