The Gambian presidency has posted footage on Facebook of the 56-year-old taking his oath of office.
The opposition United Democratic Party (UDP) had challenged the results of the 4 December election that saw Mr Barrow win with 53% of votes.
The UDP had said the vote was marred by widespread irregularities.
On Monday, the Supreme Court upheld its 28 December ruling, dismissing the opposition's petition.
Mr Barrow is a successful property developer who once worked as a security guard in London. He sprung a major surprise by defeating Yahya Jammeh during the last presidential vote in 2017.
Mr Jammeh's 22-year rule was marked by allegations of abuse, with witnesses telling a truth commission after he went into exile about state-backed execution squads and Aids patients being forced to take bogus cures.
