Passing by 521 votes to 73, the result is a huge relief for Boris Johnson, who had repeatedly missed self-imposed deadlines for the talks, and also announced he was walking away from them despite them actually continuing.
Mr Johnson had insisted the deal would give “certainty” for business and urged MPs to back it.
He said: “The purpose of this Bill is to accomplish something that the British people always knew in their hearts could be done and yet which we were continually told was impossible – we were told we could not have our cake and eat it – namely that we could trade and co-operate with our EU neighbours on the closest possible terms as we will while retaining sovereign control of our laws and our national destiny.
“We are going to open a new chapter in our national story, striking free trade deals around the world and reasserting global Britain as a liberal outward-looking force for good.
“I hope and believe that this agreement will also serve to end some of the rancour and recrimination that we’ve had in recent years, allow us to come together as a country, to leave old arguments, old desiccated, tired, super-masticated arguments behind, move on and build a new and great future for our country.
“Because those of us who campaigned for Britain to leave the EU never sought a rupture with our closest neighbours, we never wanted to sever ourselves from our fellow democracies beneath whose soil lie British war graves in tranquil cemeteries often tended by local school children, a testament to our shared struggle for freedom.
“Now with this Bill we’re going to become a friendly neighbour, the best friend and ally the EU could have.”
The deal will now go the Lords where it is expected to pass without any amendments later tonight, before getting royal assent in the early hours.
In a heated debate, SNP Westminster leader Ian Blackford, whose party voted against the deal, earlier labelled the agreement an act of “economic vandalism” and a “betrayal” on fisheries.
He said: “This deal means fewer access to fish than under the existing arrangements. Let me say that again, less access to these fish than under the Common Fisheries Policy.
“The Scottish Tories said that tying fishing to a trade deal was a red line that must not be crossed, but yet here we are – it is exactly what has been done.
“Another Brexit bubble that badly needs bursting is the myth that leaving the EU will somehow make it easier for businesses to trade.
"This is literally the first trade deal in history that puts up barriers for business instead of removing them.
“Every single Tory promise, every red line has been blown out of the water. Countless broken promises and not even one resignation.”
The SNP’s Westminster leader claimed Scotland was part of Europe before Britain and would be seeing to rejoin.
He continued: “If this whole Brexit saga was truly about sovereignty, then the Scottish people can’t and won’t be denied our sovereign right to that self-determination.
“No democrat should stand in the way of that. Nobody in this House, or even Boris with a small ‘b’.
"The Tory denial of democracy is a position that can’t and won’t hold. Scotland will have the right to choose its own future.”
SNP MP Kirsty Blackman said the deal was a "steaming mug of excrement".
Labour leader Sir Keir Starmer branded the EU agreement “thin”, but ordered his MPs to back it.
He said: “It’s often said there’s nothing simple about Brexit, but the choice before the House today is perfectly simple.
"Do we implement the treaty that has been agreed with the EU or do we not?
“That is the choice. If we choose not to, the outcome is clear, we leave the transition period without a deal, without a deal on security, on trade, on fisheries, without protection for our manufacturing sector, for farming, for countless British businesses and without a foothold to build a future relationship with the EU.
“Anyone choosing that option today knows there is no time to renegotiate, there’s no better deal coming in the next 24 hours, no extensions, no humble addresses, no SO24s, so choosing that option leads to one place – no deal.”
Despite voting for it, Sir Keir also warned that British businesses will now face “an avalanche of checks”.
He said: “Every business I have spoken to knows this and every business any member has spoken to knows this. That is what they are talking about, it is there in black and white in the treaty.
“There will be checks for farmers, for our manufacturers, for customs, on rules of origin, VAT, safety and security, plant and animal health and much more.
“Many British exporters will have to go through two regulatory processes to sell to existing clients in the EU.”
The deal was also criticised by former Prime Minister Theresa May, who suggested it was worse than the one her party repeatedly refused to back.
In a dig at Sir Keir, she said: “He said he wanted a better deal.
"He had the opportunity in early 2019 when there was the opportunity of a better deal on the table and he voted against it, so I will take no lectures from the leader of the Opposition on this deal.”