Agreement was reached "after Moscow dropped a demand for a reference to the treatment of Russian-speaking minorities in incoming members Latvia and Estonia," the paper said.
On May 1, the EU will expand from 15 to 25 nations. Five of its 10 new members are former Soviet satellites and three more were republics in the old Soviet Union.
Under the deal, the EU agreed to drop customs duties on cargo shipments between Russia and its Baltic enclave of Kaliningrad, which is cut off from the rest of Russia by Lithuania and Poland, the Moscow Times said.
The agreement will also lower trade tariffs between Russia and EU members and raise Russian steel quotas, the paper said. Russia also agreed to continue supplying fuel to nuclear power plants in the new EU member states,
it said.