In a sign of divisions within the pan-Arab body, however, Qatar voiced reservations over Abul Gheit's candidacy due to his "hostile positions" towards Doha, Arab diplomats said.
"The consultations resulted in the nomination of Ahmed Abul Gheit to the post of secretary general," Bahraini Foreign Minister Khaled bin Ahmed Al-Khalifa announced in televised remarks at the end of a ministerial meeting.
Abul Gheit, who served as foreign minister under Egypt's ousted president Hosni Mubarak, takes office at a time when the Cairo-based Arab League is facing several tests of its unity.
At the top of the list is the war in Syria that has killed more than 270,000 people and displaced millions since it erupted in 2011.
The more than five-year-old conflict has seen regional heavyweights Saudi Arabia and Iran backing opposite sides.
In addition, relations between Qatar and Egypt, which traditionally chooses candidates for the post of secretary general, have soured.
Cairo accuses Doha of supporting its outlawed Muslim Brotherhood movement of former Egyptian president Mohamed Morsi, who was toppled by the army in 2013.
The Brotherhood has been the target of a brutal crackdown since then, and Doha has regularly denounced the operations that left hundreds dead and thousands in jail.
Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al-Thani expressed Doha's "reservations" over Abul Gheit but voiced hope the next secretary general "will maintain contact between all Arab countries in the interest of joint Arab action."
Several diplomats told AFP that Qatar had accused Abul Gheit of pushing Egypt to boycott a Qatari-proposed Arab summit in 2009 to discuss an Israeli assault on Gaza.
Unlike the charismatic ex-chief of the Arab League, fellow Egyptian Amr Mussa, who was known for taking a tough stand on Israel, Abul Gheit has often faced criticism for adopting a softer approach towards the Jewish state.
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Abul Gheit had accused the Palestinian Islamist movement Hamas which rules Gaza of being responsible for the Israeli assault.
Cairo proposed Abul Gheit, 73, for the post after the incumbent, Nabil al-Arabi, another Egyptian, declined a second five-year term as secretary general. His term ends in July.
Traditionally, the secretary general has held the position for two terms and the post has gone to an Egyptian, with Tunisia's Chedli Klibi the sole exception.
Differences within the 22-member organisation, in which Syria's membership was suspended in 2011 because of its conflict, hint at a wider disunity between Arab states.
While Iran has sent thousands of "military advisers" into Syria in support of the Damascus regime, Saudi Arabia supports Islamist rebels fighting President Bashar al-Assad's forces.
Saudi Arabia and several Gulf states have since made diplomatic moves against Lebanon, whose Shiite Hezbollah movement is fighting in support of Assad.
Sectarian rivalry is also evident in Yemen, where Iran-backed Shiite rebels are fighting a Saudi-led military campaign.
The United Nations says that more than 6,000 people have been killed in Yemen since the Saudi campaign against the rebels was launched a year ago.
The rise of the jihadist Islamic State group, which has swathes of territory in Iraq and Syria under its control and is rapidly expanding its foothold in Libya, has emerged as the biggest threat to the region's stability.
To combat IS, Egyptian President Abdel Fattah al-Sisi proposed setting up a joint Arab military force, but the plan has faced resistance from within the League after it was initially adopted.
Abul Gheit will be the eighth secretary general of the League since it was founded in 1945.