But what will actually happen in the next 24 hours and beyond? And is the political chaos of the last three years really over? We take a look at what lies on the horizon.
What changes now Brexit has happened?
Barely anything will change in day-to-day life for people in Britain this year.
That’s because the withdrawal agreement simply sets the terms of Britain’s exit, and starts a so-called standstill transition period to last until December 31.
That means the UK will stay in the European single market and customs union and EU laws will still apply until the end of the transition.
Free movement of people will also continue for that period, meaning people’s holidays will not be affected.
Perhaps the biggest change is the UK will be able to start negotiating its own free trade deals with countries.
Blue passports will also begin to be issued, alongside the 50p Brexit coin.
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The UK will no longer have seats at the European Parliament, Commission or Council, where laws will be made which still affect this country, no matter how close or loose a trading relationship it decides to have in the future.
Britain will also no longer sit with the EU at international meetings, and will engage with Brussels as it does with other countries around the world.
In the Belgian city, the UK’s permanent representation (UKRep) will be replaced by a new organisation called the UK mission to the European Union (UKmis), in line with other countries.
Tim Barrow will become the UK’s ambassador to the EU.
So what actually happens now?
More Brexit negotiations.
And not only more negotiations but far more significant, deep and potentially fractious negotiations than what has gone before – as they will determine the UK’s future for years to come.
The future relationship talks will cover trade, travel, environmental protections, worker’s rights, fishing rights, financial services, security, data and much more.
Both sides are expected to waste little time in setting out their stalls.
Irish deputy PM Simon Coveney has confirmed the European Commission will publish its draft negotiating mandate on Monday.
Government sources are promising to take a different approach to negotiations than the first phase, when Theresa May’s insistence on not giving a “running commentary” allowed Brussels to set the agenda.
So Boris Johnson is expected to be fairly quick out of the blocks in publishing his own negotiating objectives to ensure the EU does not set the terms of talks in public.
Taking a leaf out of May’s book, a big Brexit speech is also planned.
The government also believes it can take advantage of the EU’s drawn-out process for finalizing its negotiating position, which will not be set in stone until February 25, having passed around all 27 EU countries, by kickstarting trade talks with the U.S. in the meantime in an effort to gain leverage in the Brexit talks.
Who are the key players in Brexit?
EU chief Brexit negotiator Michel Barnier will continue in his job, while Clara Martínez Alberola takes over as his deputy from Sabine Weyand.
On the UK side, there are bigger changes as the Department for Exiting the EU (DExEU) is now defunct and Brexit secretary Stephen Barclay out of a job.
Rather than replacing Barlcay with another minister, Johnson’s chief Brexit “sherpa” David Frost will lead the talks.
And DExEU will be replaced by a new 40-strong “task force Europe” team based in No.10 and headed up by Johnson.
Cabinet office minister Michael Gove will resume his key role preparing the UK for the end of the transition period, with another cliff-edge looming if the government fails to reach a deal with the EU.
Britain will also need to pass a number of new laws to ensure new immigration, agriculture and fisheries systems, among others, are in place for 2021.
What will be the major flashpoints?
Boris Johnson has made it illegal to extend the transition period beyond December 2020, meaning there is very little time to get a deal done.
EU sources have indicated that negotiations will need to be wrapped up around October for the European Parliament and other institutions to have time to sign off on whatever deal emerges.
That leaves at best around seven to eight months – which most experts say is nowhere near enough time to conclude a comprehensive free trade deal.
So the first big argument is likely to focus on what to actually argue about in the limited time available.
The central debate of the entire exercise will then be on how much the UK is willing to align with EU rules in return for market access.
Brussels wants the UK to sign up to a so-called level playing field to ensure it does not undercut EU worker’s rights, environmental protections and state aid rules.
But Johnson has pledged “no alignment” and has all but ruled out a level playing field.
The UK and EU have also technically agreed in the political declaration which accompanies Johnson’s deal to conclude agreements on fish and financial services by July.
And senior figures including Irish PM Leo Varadkar have suggested the UK will have to trade fishing rights for access to European markets for financial services.
Downing Street has not ruled out that possibility, insisting only that the UK will have the right to control who fishes in its waters, but is likely to push back on the timetable, which is not legally binding.
The Times meanwhile reported this week that the EU is going to play hardball in the negotiations and try and lock a role in for the European Court of Justice (ECJ) to oversee the terms of any deal, which Johnson is unlikely to agree to.
What about Northern Ireland?
While the negotiations go on, Boris Johnson’s withdrawal agreement will need implementing.
This includes provisions on EU citizens’ rights, the payment of the £39bn “divorce bill”, and most significantly new arrangements for Northern Ireland.
The PM has promised not to impose checks on goods travelling between Great Britain and Northern Ireland – but this is exactly what the deal states he must do.
But he has been warned that the EU “will not tolerate any backsliding or half measures” – setting up a potentially almighty clash.
Will we get a trade deal with the United States?
Donald Trump has said he is ready to do a “massive” free trade deal with the UK after Brexit and negotiations are expected to run in parallel with the Brexit talks.
But in reality the type of deal that can be done will depend on the UK-EU deal, and these things take years to sort out, so we are unlikely to see a big, deep deal any time soon.
Will there be more political chaos in the UK?
Johnson’s thumping general election victory, in which he secured an 80-seat majority, means we are unlikely to see the kind of parliamentary chaos witnessed in recent years.
There are unlikely to many, if any, knife-edge votes – perhaps unless he makes concessions so great that the Tory European Research Group (ERG) of hard Brexiteers, which has gone into semi-retirement as a political force, are suitably energised.
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