Discussing the withdrawal of the final 20 unarmed observers, Martha Freeman, an OSCE spokeswoman, said: "The mission is discontinued and the mandate for the monitors has expired.
"There is no longer a presence on the ground, but the OSCE will still be involved in security matters here."
Talks on extending the OSCE mission's mandate after last August's war failed, with some OSCE members accusing Russia of impeding negotiations.
Moscow insisted that South Ossetia and Abkhazia, another breakaway region, be recognised as separate from Georgia.
Russia has been building military bases, storage facilities for supplies, and roads in both the regions after it went ahead and unilaterally recognised them as independent on August 26, 2008.
Around 6,000 Russian troops are based in each region.
Nalbandov said: "It is Russia's deliberate policy to deprive the international community of the possibility of knowing what is happening on the occupied territories, concerning Russia's illegal armed presence in Abkhazia and South Ossetia, and concerning human rights violations there."
Last month, Russia also vetoed the extension of a UN monitoring mission, comprising 130 personnel, that had been active in Abkhazia for 16 years.
Edmond Mulet, the UN assistant secretary-general for peacekeeping operations, was quoted by Abkhaz media as saying that UN military and police monitors would also start leaving with immediate effect and complete their exit by July 15.
About 20 UN monitors were reported to have left on Tuesday, with the withdrawal of monitors said to be going ahead in batches.
A mission of about 225 monitors from the European Union, established after the war, will continue to operate near Abkhazia and South Ossetia, but the EU has so far been denied access to the breakaway regions.
Despite losing its presence on the ground, the OSCE will remain a partner in foreign-backed talks in Geneva aimed at preventing another conflict in Georgia.
The next round of talks in Geneva is planned for Wednesday.
Russia sent troops and tanks deep into Georgia last year to repel a Georgian military attempt to retake South Ossetia, which had received extensive backing from Moscow since breaking from Tbilisi's control in the early 1990s.
Moscow later mostly withdrew its troops into South Ossetia and Abkhazia but Tbilisi is angry at the continued presence of thousands of Russian troops in both regions.
Russia has said that this week's military manoeuvres north of the Georgian border, involving 8,500 of its troops and nearly 200 tanks, will focus on counter-terrorism and the defence of strategic targets.
In July, Nato invited condemnation from Russia by staging similar exercises in Georgia itself.