Saturday's election, the first since former dictator Yahya Jammeh fled into exile, is seen as crucial for the young West African democracy.
Crowds of Barrow's supporters marched through the streets of the capital 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 called on his supporters to respect those who voted for his opponents in a "free, fair and transparent election".
