King Salman telephoned Aoun to wish him success, "stressing the kingdom of Saudi Arabia's support for Lebanon and its unity", the official Saudi Press Agency reported late Tuesday.
Lebanese lawmakers elected the 81-year-old former army chief on Monday, ending a two-year vacancy caused by a deadlock between Iran- and Saudi-backed blocs in parliament.
Aoun had received the unstinting support of Iran's Lebanese ally, Shiite militant group Hezbollah, which Saudi Arabia blacklisted as a "terrorist organisation" in March.
His election followed a surprise U-turn by two key leaders of the pro-Saudi camp -- billionaire Sunni former prime minister Saad Hariri and Christian Lebanese Forces leader Samir Geagea.
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Hariri's influence in Lebanon has waned as his construction firm Saudi Oger has been hit by a slowdown in Saudi government infrastructure spending in what has been seen by some as a disengagement by his longtime sponsor.
Saudi Arabia's relations with both Hezbollah and its ally Iran have deteriorated sharply this year amid deep differences over the conflict in Syria.
Hezbollah has sent thousands of fighters to back President Bashar al-Assad. Riyadh supports the rebels.
Earlier this year, the kingdom halted a $3 billion programme of military aid to Lebanon to protest what it said was "the stranglehold of Hezbollah on the state".
It also urged its citizens to leave Lebanon and avoid travel to the country.