The pact – which would bind the three countries more closely to the West both economically and politically – is at the heart of the crisis in Ukraine.
Russia said that while the signing of the deal was the right of any state there could be grave consequences.
A ceasefire with pro-Russian rebels in east Ukraine is due to end on Friday.
Ukrainian President Petro Poroshenko hailed the signing as Ukraine’s most historic day since independence in 1991, describing it as a “symbol of faith and unbreakable will”.
Petro Poroshenko also said he saw the signing as the start of preparations for joining the bloc.
“Ukraine is underlining its sovereign choice in favor of membership of the EU,” he said.
Meanwhile European Council President Herman van Rompuy described it as a “great day for Europe”.
“The EU stands by your side, today more than ever before,” he told leaders of the three countries, adding that there was nothing in the agreements that might harm Russia in any way.
Meanwhile, Russian Deputy Foreign Minister Grigory Karasin told Interfax news agency that the move was fraught with difficulties.
“The signing of this serious document is, certainly, a sovereign right of each state,” he said.
“[But] the consequences of the signing by Ukraine and Moldova no doubt, will be serious.”
Earlier senior Kremlin adviser Sergei Glazyev described Petro Poroshenko as a “Nazi” and said his presidency was illegitimate because parts of Ukraine did not vote in the May elections.
Sergei Glazyev also said that Petro Poroshenko had no constitutional right to sign the treaty, which would damage the Ukrainian economy.
However, President Vladimir Putin’s spokesman Dmitry Peskov told Russian media that Sergei Glazyev’s comments did not reflect the official Kremlin position.
Petro Poroshenko’s predecessor Viktor Yanukovych refused to sign the deal under pressure from Russia and protests led to his overthrow.
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