The EU ratification will trigger the entry into force of the first-ever universal, legally-binding global climate deal.
The vote follows a decision by EU ministers on 30 September to fast-track EU ratification of the landmark agreement.
The decision permits the European Commission to deposit its ratification instrument with the UN, pending member state ratification as soon as possible afterwards.
The outcome of the vote in Strasbourg on Tuesday was widely welcomed, including by outgoing UN Secretary General Ban Ki-moon. Addressing a news conference, he hailed the ratification as a "historic moment."
He said the agreement had now been backed by those countries which represent 52 per cent of global greenhouse gas emissions.
The official also praised MEPs who, in signing the deal, had "underscored their commitment" to international cooperation.
Further comment came from Ségolène Royal, the French environment Minister who is also COP21 President.
She said, "This is a great day for Europe and a great day for the planet."
She added, "When the world is falling into violence, we have shown we can fight for the environment and this is an opportunity to be grasped.
"We must now move from pledges to action and step up the pace of change."
Others were quick to respond, with European Green Party Co-Chair Monica Frassoni, saying, "The EU must now deliver accordingly: we await an equal ambition and determination from the part of the Commission in delivering before the end of the year an ambitious energy union legislative package, in line with the just ratified commitment of pursuing the goal of keeping global temperature increase at 1.5°C.
"Targets we have on the table now for renewable energy sources and energy efficiency are far from enough."
Further reaction came from Scottish MEP Ian Duncan, the Conservative energy and climate change spokesperson, who said, "Doubts have been cast about the EU's ability to ratify the agreement on time ever since the deal was struck in Paris last December. I am pleased to see that the Commission and the Council have finally committed to action."
Elsewhere, EPP group leader Manfred Weber said: "Without the EU and Europe's strong position on climate, the Paris agreement would never have happened. Europe is setting the benchmark on climate protection.
"To keep this leading role, member states should stick to the existing ambitious goals and swiftly implement the agreement. It is crucial that we do not waste any more time."
There had been fears the EU would lose its leadership role in climate change after the US, China and India all agreed to ratify the agreement ahead of the EU.
The agreement comes into force when 55 per cent of countries representing 55 per cent of global emissions deposit their ratification instruments with the UN.
With the EU's decision to ratify the agreement, these thresholds have now been met.
It is now up to every member state to ratify the deal individually.
In some EU countries, such as Belgium, this means putting the matter to a vote in several parliaments. The deal reached in the Council and endorsed on Tuesday by Parliament commits all EU member states to ratify the agreement "as soon as possible."