Anerood Jugnauth, who has presided over steady economic growth, said in a televised speech he would continue to serve in government in another, unspecified capacity.
“The time has come for the country to have a young leadership that represents the future,” he said. “I ask the population to support Pravind Jugnauth as it did for me.”
A veteran politician, Anerood Jugnauth was appointed prime minister in December 2014 after Lepep, an alliance of three political parties, won three-quarter of the seats in parliament.
In December, one of the three parties quit the coalition after a row with government over a bill regarding prosecutions, but the remaining two-party alliance still enjoys a parliamentary majority.
Pravind Jugnauth, 55, is expected to be named prime minister early next week.
Famed for its white sand beaches and luxury spas, the Indian Ocean island nation of Mauritius is diversifying its economy away from sugar, textiles and tourism into offshore banking, business outsourcing, luxury real estate and medical tourism.