Bihi, 69, won with 55 percent of the vote, beating Abdirahman Iro of the main opposition Waddani party, who received 41 percent. Faysal Ali Warabe, who previously ran and lost in 2010, came third with four percent.
"The tallying process of the election was concluded and Kulmiye party candidate Muse Bihi Abdi... won the election and will be the president," said election commission chairman Abdikadir Iman Warsame.
The northern territory, which declared independence from the rest of Somalia in 1991, hopes the successful conclusion of its third presidential election will bolster its democratic credentials and strengthen the case for independence from its troubled neighbour.
Elections are meant to be held every five years, but the poll was delayed for two years due to drought and technical issues.
More From This Section
Somaliland's history of peaceful, credible elections and democratic transition sets it apart from anarchic southern Somalia.
Somalia -- which is wracked with fighting between African Union-backed Somali forces and the Al Qaeda aligned Shabaab militants -- held an election in February that saw a president chosen via a limited electoral process in which handpicked clan elders selected delegates who were allowed to vote.
Iro had also questioned the conduct of this month's election, claiming harassment and fraud, including the participation of underage voters.
Somaliland, a former British protectorate, won independence in 1960 but days later joined with Somalia.
In 1991, after years of bitter war with the government in Mogadishu, it declared independence from the rest of the country, and has long hoped for international recognition.