"It's a historical moment, albeit a sombre moment, for us. We deeply regret this outcome", committee chair Antonio Tajani said after the 23-3 vote.
Prime Minister Boris Johnson had refused to accept any changes to the Withdrawal Agreement Bill, which will enact Britain's departure from the European Union, facing down opposition lawmakers who say he has hardened its terms.
After three more months of bitter deadlock and division, which many argued was perpetuated by Mr Johnson's rhetoric, an election was called and he gained a huge Conservative majority of 80.
The House of Lords made changes to the bill on Tuesday.
And so the Bill was passed by parliament and yesterday was given Royal Assent by Her Majesty.
In recent weeks, Cabinet ministers and the us ambassador to the UK Woody Johnson have said that the government should pursue an American trade deal to put pressure on Brussels.
The Scottish National Party says Scotland should hold a referendum on independence from the United Kingdom, which Johnson refuses to allow. Johnson has repeatedly insisted that he will not extend the transition period.
Once the European Parliament gives its consent, the Council will conclude the agreement on behalf of the EU.
Steven Mnuchin, the US Treasury Secretary pictured in Davos, Switzerland today, said of a trade deal with the UK: 'We look forward to getting that done this year'.
They said other elements could be negotiated and added later because only a "bare bones" deal is possible in such a short time.
The UK's relationship with the bloc is set to remain unchanged during an 11 month transition period in which negotiators will thrash out details on the future relationship, including new agreements on security, trade and free movement.
Johnson will now be responsible for defining the terms on which Britain trades and shares everything from data to fishing waters with the remaining 27 European Union member states.
The EU Parliament is expected to ratify the Brexit divorce deal next Wednesday just days before the deadline.
The European Commission on Friday published a slideshow which includes two maps which provide examples of where these customs checks on goods will take place between Great Britain and Northern Ireland in both directions.