A majority of lawmakers had to decide on whom to name as premier before Aoun tasked the candidate with forming a government.
According to a Reuters tally of votes cast by lawmakers in official consultations, Adib secured the support of a majority of lawmakers to be designated as the new prime minister.
Adib secured at least 66 votes, or more than half of the 120 MPs currently serving in the Lebanese parliament, after the Christian Free Patriotic Movement announced it had nominated him.
Lebanon's parliament usually has 128 MPs but eight resigned following the Aug. 4 port explosion.
A relatively unknown 48-year-old diplomat, Adib, a close aide to former premier Najib Mikati, is about to form a government after he secured backing from the country's politicians.
On Sunday, the Sunni Muslim political figures in Lebanon, including the Future Movement party headed by former premier Sa'ad Hariri, picked Adib to succeed Hassan Diab, who resigned as prime minister following Beirut’s blast.
Under a power-sharing agreement that ended the 1975-1990 civil war in Lebanon, the prime minister must be a Sunni Muslim, the president a Maronite Christian and the parliament speaker a Shia Muslim.
Hariri announced on Monday that he had nominated Adib to the position in formal consultations with Aoun.
Speaking after a meeting with the president, Hariri said the new government should be formed quickly and made up of specialist ministers.
Hezbollah members of Lebanon's parliament also nominated Adib as the next premier.
Hezbollah’s parliamentary bloc “informed President Aoun of its agreement to the nomination of Mustapha Adib and we expressed our readiness for positive cooperation,” the head of its parliamentary bloc, Mohamed Ra'ad, said after a meeting with the president on Monday.