President Barrow's plane touched down at Banjul airport where jubilant crowds waited to welcome him.
Mr Barrow, who has been in neighbouring Senegal, won elections in December.
However a handover was stalled when Mr Jammeh, Gambia's president of 22 years, refused to step aside.
He left for exile at the weekend after mediation by regional leaders and the threat of military intervention.
Mr Barrow, dressed in white robes and a cap, stepped off the plane in Banjul as heavily armed troops from Senegal and Nigeria stood by.
Overhead, a fighter jet from the West African force guaranteeing the new president's security performed fly-pasts.
"I am a happy man today," Mr Barrow told a reporter from the Associated Press in the crush at the airport, adding: "I think the bad part is finished now."
The president said his priority was to appoint his cabinet and "then get the ball rolling".
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