Barrow took refuge in Senegal after his defeated rival Yahya Jammeh refused to cede power following the Dec. 1 election.
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.
Barrow told reporters that he intended to name his cabinet "very soon", reform the constitution and establish a truth and reconciliation commission to investigate the past regime.
Hundreds gathered at the airport awaiting Barrow's arrival, with drummers and dancers firing up the crowds as Nigerian and Senegalese soldiers looked on.