Adama Barrow says he will be sworn in as Gambian president at the country's embassy in neighbouring Senegal.
The message, posted on his social media accounts, invited the general public to attend the ceremony.
Last-ditch mediation efforts by regional leaders to convince Yahya Jammeh to step down as president ahead of the inauguration failed overnight.
He 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 holidaymakers.
Media captionThe rise and fall of Yahya Jammeh
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.
At least 26,000 Gambians, fearful that violence could erupt, sought refuge in Senegal this week.
Meanwhile, thousands of UK and Dutch tourists continue to be evacuated from the tiny West African state.