Hansjoerg Haber, who is heading the EU observer mission, instructed the monitors to be friendly and show confidence.
Many observers are also experts on human rights and legal issues and will be unarmed and not be let into the buffer zones until Moscow completes its pullback by 10 October.
Russia’s slow withdrawal was agreed in a ceasefire deal brokered by French President Nicolas Sarkozy.
But Russia plans to keep nearly 8,000 troops in Abkhazia and South Ossetia, which it has recognised as independent states.
The international community, especially the European Union and the United States, has condemned both the buffer zones and Russia's recognition of the two regions.
The EU wants its observers to have access to the breakaway regions, but Russia has refused.
EU observers will be based in four field offices, in the capital Tbilisi, in Gori (just south of South Ossetia), in Zugdidi (near the Abkhaz border) and Poti.
The conflict in the region began on 7 August when Georgia tried to retake South Ossetia by force after a series of lower-level clashes.
Russia launched a counter-attack against Georgia and ejected Georgian troops from both South Ossetia and Abkhazia.
The brief war caused the death of thousands of people and 200,000 refugees.
An international donors' conference is scheduled for Brussels next month to help Georgia rebuild.
The United States pledged US$ 1 billion in aid to Georgia; the European Union is expected to match that sum, money which Georgia will not be allowed to use to rebuild its military.