Once the comprehensive economic and trade agreement (CETA) is fully implemented, around 92 per cent of EU agriculture and food products will be exported to Canada tariff-free.
Approval for the deal comes despite warnings that the agreement could lead to a "bonfire" of environmental, health and social protection standards.
The committee voted on Tuesday 25 to 15 in favour of the deal, with one abstention.
The agreement will now be put to a vote by Parliament as a whole at the February plenary session in Strasbourg. If, as expected, it is approved, CETA could apply provisionally from as early as April, although it also has to be ratified by national and regional parliaments.
The decision was greeted by the rapporteur on the issue, Artis Pabriks, a centre right Latvian member, who said, "By approving CETA we take a significant step forward. In the face of rising protectionism and populism, Parliament is able and willing to act on behalf of European citizens.
"Ratifying this agreement with Canada will enable trade to continue to bring wealth to both shores of our transatlantic friendship. The duty of our governments is to ensure that each and every one of us benefits from this wealth."
Conservative international trade spokesperson Emma McClarkin also welcomed the outcome, saying CETA would "help restore the EU's reputation as a reliable trading partner."
The deal had been held up by politicians in the Belgian region of Wallonia.
"This is one of the highest quality agreements ever negotiated and clearly highlights the benefits of free trade," said McClarkin.
"CETA will eliminate 99 per cent of tariffs between the EU and Canada, save EU exporters €500m a year and increase trade by 20 per cent.
"It took the EU far too long to reach this stage and hopefully lessons have been learned about how future trade deals should be conceived, negotiated and ratified."
The vote was also welcomed by ECR group shadow rapporteur David Campbell Bannerman, a British deputy, who said the deal "will give EU companies access to Canadian procurement markets, something that Canada has never allowed before. In addition, it contains welcome new elements, such as a mechanism to allow for mutual recognition of professional qualifications."
Parliament's EPP group spokesperson on the trade committee, Daniel Caspary said, "The logic of CETA is as simple as it is convincing: more trade means more growth, more and better jobs and higher salaries.
"The sooner Europeans profit from it, the better. Everyone has understood this at this stage except the trade-hostile groups in Parliament, who held CETA hostage for months without any factual reason."
Elsewhere, the response was less enthusiastic.
Anne-Marie Mineur, the GUE/NGL shadow rapporteur, said, "I am disappointed and worried the committee has voted in favour of the CETA agreement. It is a terrible agreement for many reasons.
"Not only is there very little basis for all the big promises of jobs and economic growth, yet huge risks for our labour rights, environmental protection and consumer rights, but there are also still a lot of loose ends in the dossier. The lack of democratic involvement and minimal transparency also set an alarming precedent for trade agreements to come."
Further concern was voiced by Greenpeace EU trade policy adviser Shira Stanton who said, "The trade committee's recommendation is disappointing but not surprising. After years of indoctrination on this new breed of investment protection deal, many politicians are reluctant to stick their necks out.
"They label any criticism as a capitulation to populism, but an honest look at the evidence would force them to recognise that multinationals are gearing up for an assault on nature, on our health and on social rights.
"MEPs have one last chance in February to reject this corporate power grab. They should take it to protect the planet and the people who elected them."
The committee vote took place a day after US President Donald Trump's withdrawal from the trans-Pacific partnership trade agreement.
Reacting to this, European trade Commissioner Cecilia Malmström said, "Those who in the 21st century think that we can become great again by rebuilding borders, re-imposing trade barriers, restricting people's freedom to move - they are doomed to fail.
"The election of Donald Trump seems likely to put our EU-US negotiations firmly in the freezer."