In a phone conversation, Aboul-Gheit congratulated Hassan Sheikh Mohamud on his election as the new president and discussed means of supporting Somalia on its path to political reconciliation and stability.
He expressed the Arab League's support for Somalia in combating all challenges, especially the threat posed by terrorist groups.
"The historical elections will be a turning point for promoting stability and security in Somalia and will help get Somalia constructively involved in the international community," the Arab League chief said.
Aboul-Gheit reiterated his confidence in Mohamud's ability to meet challenges and crises through his wide range of experiences, including serving as Somalian president from 2012 to 2017.
Mohamud was confirmed to have defeated incumbent President Mohamed Farmajo by 214 votes against 110 in a third-round runoff on May 15.