Hariri's appointment as prime minister is meant to build on the momentum that followed Aoun's election on Monday. Lebanon has had no president for more than two years, since Michel Suleiman's term expired in 2014.
Aoun, a Maronite Christian and a former general, was elected Oct. 31.
Hariri served as prime minister between 2009 and 2011. His administration collapsed after Hezbollah and its allies chose not to cooperate in the government. He must build a consensus in a country split along religious lines and enduring economic hardship because of the war in adjacent Syria. The Lebanese economy has struggled with the arrival of 1.5 million Syrian refugees, and the war has blocked Lebanon's only overland trade route. Tourism has also suffered.
In a televised speech, Harari said it was necessary to work quickly to form a government of national unity and restore trust in the country.
"We owe it to the Lebanese people to start working as soon as possible to protect our country from the flames burning around it," he said.