Two other designates gave up after failing to form governments in Lebanon’s complex system of sectarian power-sharing, and it took Mr. Mikati more than six weeks to succeed, an effort that included more than a dozen meetings with Mr. Aoun.
Mr. Mikati has served as prime minister twice before, most recently from June 2011 to May 2013, a background that critics said made him part of the political elite that had driven the country into the ground and an unlikely figure to press for wide-reaching reforms.
His 24-member cabinet contained only one woman, the minister of administrative development. The rest included some figures with clear ties to the country’s main political parties as well as some outsiders.
Lebanon has sought aid from the International Monetary Fund, the United States, France and other countries, but most promises of assistance have been contingent on the formation of a government and on the implementing of measures aimed at increasing transparency in a country where systematic corruption is a perennial problem.
It was not clear what immediate steps Mr. Mikati would take to stem a crisis whose causes have been accumulating for many years, but he said he would solicit aid from other Arab countries.
Traditionally, countries such as Saudi Arabia have invested heavily and supported preferred political parties in Lebanon, but much of that support has dried up as foreign backers have grown tired of the country’s perpetual dysfunction.