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Transnistria is a disputed territory with separatist ambitions in Moldova, but is not recognized as a sovereign country by the international community.
The agreements continue a dramatic reverse to past Russ- Ukrainian government relations which began after Yanukovych took office in February.
Yanukovych said the presidents agreed that their new-found friendship would not be used to gang up against other countries. " All decisions will be taken to protect our national interests," he said.
Monday's talks were watched for signs of progress on Russia's proposal to merge the assets of its state gas monopoly, Gazprom, and Ukraine's Naftogaz.
The proposal from Russian Prime Minister Vladimir Putin has sparked criticism from the Ukrainian opposition, which saw it as an attempt by Moscow to wrest control over the country's most valuable industrial asset.
Yanukovych said the merger should leave two sides with equal stakes in the new company, defying Russia's demand for control.
No agreement on the merger was signed during Medvedev's trip, but Gazprom chief Alexei Miller said talks on the issue are continuing. He told reporters that Gazprom would fully modernize Ukraine's aging gas transportation system if the merger took place.
On the same day, several hundred Ukrainian nationalists held a brief protest against the pro-Russia policy of Ukraine's new leadership.
Medvedev arrive in Kiev on Monday for a two-day official visit to Ukraine.