Mr Barrow, who has been staying in neighbouring Senegal, won elections in December.
However a handover was stalled when Gambia’s president of 22 years, Yahya Jammeh, refused to step aside.
He left for exile at the weekend after mediation by regional leaders and the threat of military intervention.
Mr Barrow was sworn in as president at the Gambian embassy in Senegal a week ago, but a public inauguration on home soil is planned soon, aides say.
Mr Barrow, 51, expects a “big, big welcome” when he arrives back in Banjul. he told the International Business Times UK.
“I think it will be the biggest in the history of our country.”
He added that he was “very excited” after the “very difficult transition”.
The president is to be accompanied by the UN envoy for West Africa, Mohamed ibn Chambas. He has said the UN will help uphold security in The Gambia.
Several thousand West African soldiers remain in The Gambia amid reports that rogue pro-Jammeh elements are embedded in the country’s security forces.
The West African force had threatened to drive Mr Jammeh from office if he did not agree to go.
A new inauguration will be organised soon at the national stadium in Banjul, his spokesman Halifa Sallah said.
“It will be an occasion to show strength. Everyone will be invited. The president will address his people,” he told Senegalese radio.
Mr Jammeh, who was a 29-year-old army lieutenant when he came to power in a 1994 coup, had refused to accept the results of the December election.
After his departure, reports emerged that more than $11m (£8.8m) had disappeared from The Gambia’s state coffers.
However a presidential adviser said the police had been asked to investigate and would determine if anything was missing.
Mr Jammeh is yet to comment on the allegations.
Posted by Juliet Ekwebelam (BBC)