Much of the Georgian port's naval infrastructure had been destroyed by the Russian military during the fighting.
The Russians were required to withdraw from Poti and from the nearby town of Senaki by Monday, under the terms of a ceasefire deal brokered earlier this week by the EU.
The deal also requires the Russians to complete a full withdrawal from all bases on Georgian territory - except for South Ossetia and Abkhazia - following the planned deployment of EU monitors to the area by 1 October.
Moscow later clashed with the EU over the terms of the deal, saying it had not given EU monitors the right to enter Abkhazia and South Ossetia.
The two regions have had de facto independence since a civil war in the early 1990s, and Moscow has strongly backed their breakaway governments.
Fighting between Russia and Georgia began on 7 August after the Georgian military tried to retake the breakaway region of South Ossetia by force.
Russian forces launched a counter-attack and the conflict ended with the ejection of Georgian troops from both South Ossetia and Abkhazia.
Hundreds of people were killed in the fighting and some 200,000 were displaced - most of them Georgians.
Russian forces also set up several bases on Georgian territory outside the separatist regions, in so-called "buffer zones" - a move criticised by Georgia and the EU as a violation of an earlier ceasefire deal.
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