The message, posted on his social media accounts, invited the general public to attend the ceremony.
Last-ditch efforts by regional leaders to convince outgoing President Yahya Jammeh to step down failed overnight.
Yahya Jammeh lost elections last month, but wants the results annulled citing errors in the electoral process.
West African military forces are ready to enforce a transfer of power in The Gambia, a popular beach destination among European tourists.
Senegalese troops remain stationed at the Gambian border, despite the deadline for Yahya Jammeh to stand down passing at midnight.
The threat of military action is supported by Nigeria and other states in the region.
Adama Barrow has been in Senegal since January 15 following an invitation to attend a summit of African leaders who back his victory.
He tweeted and posted on Facebook that his inauguration would take place at 16:00 GMT at the embassy in the capital, Dakar.
At least 26,000 Gambians, fearful that violence could erupt, have sought refuge in Senegal.
Meanwhile, thousands of European tourists continue to be evacuated from The Gambia.
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