Trump stirred concerns in central and eastern Europe during the U.S. election campaign with his praise for Russian President Vladimir Putin and also his suggestion that the United States may not defend allies deemed to spend too little on defense.
Georgia wants to join NATO, though the Atlantic alliance has played down its chances and Russia, which fought a brief war with the south Caucasus nation in 2008, is firmly opposed.
Georgian President Georgy Margvelashvili told Reuters in an interview late on Tuesday that he was sanguine about the prospect of Trump taking power.
"Our relations and communication with President Donald Trump as well as with our friends and allies on the Hill (in Congress) from the Republican and Democratic sides will be maintained because we are talking about interests and ... goals that are and have been shared for the last 25 years," he said.
"We've never had concerns about our allies, we do have interests for intensifying our agenda, and we do not think that this agenda will be undermined," he said
Georgia spends around two percent of its national output on defense, the target recommended by NATO but still not met by a majority of Washington's European allies.
The administrations of George W. Bush and Barack Obama provided extensive military aid to Georgia and spoke out against what they said was Russia's lack of respect for Georgia's borders after Moscow backed two breakaway Georgian regions in the 2008 war.
A fifth of Georgian territory remains under the control of pro-Russian separatists. The country is strategically important for the West because it is criss-crossed by pipelines carrying Caspian oil and gas to Europe.