The deal came during an ongoing high-level commission visit to Moscow.
In Brussels, commission spokesman Diego de Ojeda broke the news, saying an overall deal with Russia on EU enlargement is now "very close."
"One of the outstanding issues for the Partnership and Cooperation Agreement (PCA) extension, or to agree on extending the PCA to the 25 member states, has been now dealt with, it is solved. Particularly [this refers] to [the] transit of goods to and from Kaliningrad. This is good news," de Ojeda said.
"We would like to see the integration of the Russian minorities accelerated. There are procedures in place, both countries have procedures that their citizens can adhere to and therefore achieve full citizenship."
The agreement, which RFE/RL has seen, says the EU has agreed not to levy any customs and transit duties on Russian goods going to or coming from Kaliningrad.
De Ojeda said the details of the deal will be made public next week when EU and Russian foreign ministers meet in Luxembourg. The EU hopes to sign a joint declaration with Russia which will address all Russian concerns over enlargement the bloc considers legitimate. Russia has said it will not expand its existing partnership agreement with the EU to its new member states if its concerns are not met.
Issues already resolved include Russian concerns over trade. A draft text of the joint declaration -- seen by RFE/RL -- says that the EU has agreed to extend Russia's steel quotas, ease its aluminum imports to the bloc, and relieve the application of the EU anti-dumping legislation on Russian exports. The EU has also agreed that Russia's existing contracts for the supply of nuclear materials to some of the new member states will remain valid.
De Ojeda today said the only outstanding issue is Russia's wish to jointly address the situation of the Russian-speaking minorities in Estonia and Latvia. De Ojeda said agreement on this issue is also "very close" and remains a "matter of language."
De Ojeda said the European Union remains committed to the view taken during the accession negotiations of Estonia and Latvia that both fulfill political entry criteria on democracy and human rights. He added that citizenship is primarily an issue for the member states in the EU.
However, de Ojeda said the European Union would like to speed up the integration of the Russian-speaking noncitizens into Estonian and Latvian societies.
"We would like to see the integration of the Russian minorities accelerated. There are procedures in place, both countries have procedures that their citizens can adhere to and therefore achieve full citizenship. Our other point view is that the accession to the European Union will -- if [anything] -- improve the situation of the Russian minorities," de Ojeda said.
An EU source, who spoke on condition of anonymity, said the EU-Russia joint declaration is likely to say that EU enlargement will benefit minorities within its borders, facilitate their integration, and that the bloc rules out discrimination against any minority group.
Latvia and Estonia have so far held out, rejecting all references to minorities in the joint declaration. Both have sizable Russian minorities, many of whom are noncitizens.
However, sources close to the talks have told RFE/RL both are eventually likely to accept a mention provided it does not name either country directly, to avoid blocking the overall EU-Russia deal.