Barrow's return at 1600 GMT will cap days of anxious waiting in the tiny former British colony that was thrown into chaos when longtime leader Yahya Jammeh refused to leave after losing a December 1 vote.
Barrow took the oath of office at his country's embassy in Dakar a week ago and a multinational African force then entered The Gambia to ensure his safe return home and Jammeh's departure.
Gambians said they were looking forward to their freedom after two decades of Jammeh's iron-fisted rule.
"He will be different in all aspects... We have been living under dictatorship for 22 years," added pensioner Ibrahima Gaye.
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"You can go home at night and sleep without worrying you will be arrested before daybreak," he said.
Barrow has not been seen in public and has not publicly addressed Gambians since his swearing-in.
A senior government official had told AFP that "It is important for him to come to avoid the void."
"People are very happy and it's elating".
Diplomats had urged Barrow to return quickly to curb the impact of the political crisis on the tourist-reliant economy, already in a fragile state.
The UN envoy for West Africa, Mohamed Ibn Chambas, who briefed the Security Council on The Gambia, stressed that the United Nations was working to bolster stability.
The UN official is due to fly to Banjul for Barrow's return.
Swedish ambassador Olof Skoog, who holds the Security Council's presidency, said: "We shouldn't just turn our back on Gambia now and walk away to the next situation but really make sure that we stay the course and support democracy."
Barrow will be staying at his own residence until further notice while State House, Jammeh's former seat of power, is assessed for potential risks.