Barrow garnered 53 percent of the vote, according to results released by the electoral commission late on Sunday.
Crowds of Barrow’s supporters marched through the streets of the capital Banjul to a din of horns and danced on a vast esplanade.
Barrow received a standing ovation when he addressed them with “a great sense of joy and humility” and told them to respect those who voted for his opponents in a “free, fair and transparent election”.
“I will do all I can and utilise every resource at my disposal to make The Gambia a better place for us all,” he said.
Before the full results were announced, three of Barrow’s rivals had rejected partial results.
“At this stage, we reject the results announced so far,” Darboe and two other candidates said in a joint statement earlier. “All actions are on table.”
Saturday’s election, the first since former strongman Yahya Jammeh fled into exile in 2017, is seen as crucial for the young West African democracy.
Jammeh refused to accept defeat to Barrow in the December 2016 elections.
Gambians flocked to the polling booths on Saturday to choose who would lead their country – the smallest in mainland Africa – for the next five years, with the turnout at 87 percent, according to official results.
Earlier on Sunday, Ernest Bai Koroma, the head of an election observation mission from the Economic Community of West African States (ECOWAS), appealed to all the candidates “to accept the outcome of the election in good faith”.
The election was being closely watched as a test of the democratic transition in The Gambia, where Jammeh ruled for 22 years after seizing power in a bloodless coup in 1994.
He was forced into exile in Equatorial Guinea in January 2017 after Barrow, then a relative unknown, defeated him at the ballot box.
Jammeh lost to Barrow in the 2016 election but had to be removed by military intervention from other west African states.