West African military forces are ready to enforce a transfer of power in The Gambia, a popular beach destination among European holidaymakers.Senegalese troops remain stationed at the Gambian border, despite the deadline for Mr Jammeh to stand down passing at midnight.
The threat of military action is supported by Nigeria and other states in the region.
Mr Barrow has been in Senegal since Sunday following an invitation to attend a summit of African leaders who back his victory.
The president-elect 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 UK and Dutch tourists continue to be evacuated from the tiny West African state.