Mohamud arrived at Bole International Airport on Wednesday and was received by Ethiopian Prime Minister Abiy Ahmed, who conveyed a message of welcome.
The prime minister's office stated that the two leaders and their delegations emphasized the importance of working together to improve stability in the Horn of Africa.
Both countries are facing challenges such as conflict and drought, which are fueling instability in the region.
Mohamud replaced former President Mohamed Abdullahi Farmaajo — who had previously unseated his rival in 2017 — in a rematch earlier this year during a tense, heavily-guarded election.
Following the vote, observers raised concerns about the possibly souring of relations when Mohamud failed to visit Ethiopia when touring other nations in the region.
Upon his arrival Wednesday, Mohamud said on Twitter that he had "held productive talks" with Ahmed and that the two "discussed interlocking challenges and common opportunities," adding "we are committed to Somalia-Ethiopia relations."