Also that remains is for the Queen to sign the law, a formality, then it becomes law.
The new trade arrangement comes into effect at 23:00 on December 31 replacing the Brexit transition period which has been in place since the end of January.
The deal, announced on Christmas Eve, has been rushed through Parliament so it is passed into law when this happens.
On Wednesday it was overwhelmingly backed by the House of Commons, with 521 MPs voting in favour against just 73 opposed.
As well as the Conservatives the deal was backed by Labour, with Keir Starmer arguing it was the only alternative to a no deal Brexit.
The Labour leader argued a “thin deal was better than no deal”.
The Liberal Democrats, SNP and DUP all voted against the agreement.
Just two Conservative MPs, John Redwood and Owen Paterson, refused to vote for the deal with both Brexit supporters abstaining.
However a sizable block of Labour MPs ignored their leader’s instruction and abstained on the vote.
Conservative peer Baroness Nicky Morgan tweeted: “The House of Lords has also now approved the Government’s Trade & Co-operation Agreement with the EU – I was v pleased to speak in today’s debate.
“4 and a half years after the 2016 vote it’s time to seize the moment & focus on making a success of the UK’s future outside the EU.”
However the deal received a less enthusiastic response from Lord Heseltine, a prominent Remain supporter.
On December 24 he commented: “We must welcome the news that Brexit does not end in the chaos of no deal, but only with the sense of a condemned man informed that his execution has been commuted to a life sentence.”
Whilst Britain formally left the EU at the end of January it remains in a Brexit transition period until 23:00 on December 31.
During this time the UK still has to pay into the EU budget and follow many rules made in Brussels.
In return Britain gets continued access to the European single market.
The new deal will replace this arrangement, with Boris Johnson arguing it means the UK can “go our own way but also have free trade”.
If Parliament had rejected the deal Britain would have ended up trading with the EU on World Trade Organisation terms, meaning substantial tariffs on some goods.
Speaking to the BBC’s Laura Kuenssberg Mr Johnson said: “There will be changes.
“And we’ve been very clear with people that they have to get ready for 1 January, things will work differently.
“But from the point of view of UK exporters, for instance, they’ll now have the advantage, that they’ll only have one set of forms they have to fill out for export to around the whole world.”
The Brexit trade deal was signed by European Commission president Ursula von der Leyen in Brussels.
It was then flown across the English Channel to be signed by Mr Johnson.
Britain voted to leave the EU back in June 2016.