The officers - who were released from custody on spying charges in Georgia and handed over to the Organisation for Security and Cooperation in Europe earlier in the day - boarded a Russian government plane to the city.
They were joined by two other officers sought by the Georgian authorities on spying charges. The two officers had been hiding in the Russian military headquarters.
The arrests last week infuriated Russia, which has put its troops in Georgia on high alert, recalled its ambassador and evacuated its citizens in the worst bilateral crisis between Moscow and the former Soviet state in years.
Despite Georgia's announcement that it would release the officers, Russia's transport and communications ministries said all air, road, rail, sea and postal links with Georgia would be suspended.
Earlier, the four were released from handcuffs and handed over to an OSCE delegation.
"The message to Russia is 'enough is enough'," the Georgian president, Mikhail Saakashvili, told Reuters.
"We want to have good relations. We want to have dialogue. But we cannot be treated as a second-rate backyard of some kind of emerging empire."
Yesterday, the Russian president, Vladimir Putin, accused pro-western Georgia of state terrorism and suggested that it could not count on US support.
Mr Saakashvili last night accused Mr Putin of overreacting to the arrests, saying: "I don't think they are irrational enough to use military force."
He also denied he had been prompted into provoking the crisis by the US. "Some people could consider our action as something that has been coordinated by Washington. This is not true," Reuters quoted him as saying.
"The US state department made it very clear that this is a bilateral issue between Georgia and Russia."
Russia's tense relations with Georgia have worsened since Mr Saakashvili came to power in 2003, pledging to move the country out of Russia's orbit, bring breakaway provinces back into the fold and join Nato in 2008.
Along with around 2,500 peacekeepers in the breakaway provinces of Abkhazia and South Ossetia, Russia has between 3,000 and 4,000 troops at two military bases in Georgia.
It pledged to withdraw by the end of 2008 under a deal signed last year.
