The four officers, who earlier on Monday were released from custody and handed over to the Organisation for Security and Co-operation in Europe, boarded a Russian government aeroplane in Tbilisi that was headed for Moscow, said Viktor Beltsov, the Russian Emergency Situations Ministry spokesman.
They were joined by two other officers sought by Georgian authorities on spying charges, who had been hiding in the Russian military headquarters.
It has rejected Georgia's bid to defuse the crisis by releasing the officers.
The arrests of the men 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 in years between Russia and the former Soviet state.
Earlier in the day, Russia said it would impose travel and communications sanctions on Georgia, and suspended transport and postal links.
The transport and communications ministries said that all air, road, rail, sea and postal links with Georgia would be suspended.
Georgia wants to join Nato and reduce Russian influence
Russian carrier Aeroflot said it would stop all flights to Georgia from Tuesday.
The measures came despite the imminent release of the Russian officers.
Vladimir Putin, the Russian president, had accused Georgia of "state terrorism with hostage-taking" by arresting the army officers.
Putin's comments were interpreted by Georgia's foreign ministry as a threat to use military force.
The Georgian president has, however, dismissed reports that Russia is planning to use military force.
"I don't think they are irrational enough to use military force," Mikhail Saakashvili said on Sunday.
Georgian has forged close military ties with Western states
"It is an over-reaction caused by nervousness that they have created by themselves."
Putin had also suggested on Sunday that Saakashvili should not count on his "foreign sponsors" - a reference to the US - for support in the confrontation with Russia.
Javier Solana, the European Union foreign policy chief, and the 56-member OSCE had urged a solution to the crisis.
Saakashvili, who swept to power in a popular revolution in 2003, has angered Russia by forging close military ties with Western states and saying that he wants to take Georgia into Nato.