Bush, making the first visit to Georgia by a US president, arrived on Monday aboard Air Force One from Moscow, where he took part in celebrations to mark the 60th anniversary of the defeat of Nazi Germany.
At Tbilisi airport, festooned with Stars and Stripes flags, Bush was greeted by President Mikhail Saakashvili, the pro-Western leader catapulted to power 18 months ago in a "Rose Revolution" who has since been trying to shake off Kremlin's influence.
Saakashvili boycotted the Moscow festivities because the Kremlin refused to bow to his demands for the immediate closure of two Russian military bases on Georgian soil.
Moscow has about 3000 troops in the Soviet-era bases, which Saakashvili has likened to an occupation of his country. The United States has dozens of military trainers in Georgia.
Saakashvili led the Rose
Revolution in November 2003
Speaking to reporters on board the flight from Moscow, White House spokesman Scott McClellan said Georgia was a "beacon of liberty for the region and for the world" and "an example of courage".
The main theme for talks between Bush and Saakashvili would be building lasting democratic institutions, he said.
The centerpiece of the 24-hour visit will be on Tuesday, when Bush addresses the Georgian people on Tbilisi's Liberty Square beneath a massive banner reading "Celebrating Democracy and Freedom".
It was from that square in November 2003 that crowds of people marched on Georgia's parliament, forcing the resignation of veteran leader Eduard Shevardnadze.
Georgia's peaceful revolution created the template for fellow ex-Soviet republics Ukraine and Moldova to turn their backs on Moscow and pursue integration with the West.