A new era has begun for the United Kingdom after it completed its formal separation from the European Union.
The UK stopped following EU rules at 23:00 GMT, as replacement arrangements for travel, trade, immigration and security co-operation came into force.
Boris Johnson said the UK had "freedom in our hands" and the ability to do things "differently and better" now the long Brexit process was over.
The first lorries arriving at the border entered the UK without delay.
UK ministers have warned there will be some disruption in the coming days and weeks, as new rules bed in and British firms trading with the continent come to terms with the changes.
But officials have insisted new border systems are "ready to go".
As the first customs checks were completed after midnight, Eurotunnel spokesman John Keefe said: "It all went fine, everything's running just as it was before 11pm. It's very, very quiet, there are very few trucks around, as we predicted."
The first ferry from Holyhead in Wales arrived in Dublin Port at 05:55 GMT with about a dozen lorries on board, all of which cleared customs checks for the first time without delays.
The UK officially left the 27-member political and economic bloc on 31 January, three and half years after the UK public voted to leave in the 2016 Brexit referendum.
But it has stuck to the EU's trading rules for the past 11 months while the two sides negotiated their future economic partnership.
After trade talks went down to the wire, a landmark treaty was finally agreed on Christmas Eve. It became law in the UK on Wednesday after it was approved by Parliament.
Under the new arrangements, UK manufacturers will have tariff-free access to the EU's internal market, meaning there will be no import taxes on goods crossing between Britain and the continent.
But it does mean more paperwork for businesses and people travelling to EU countries while there is still uncertainty about what it will happen to banking and services, which are a major part of the UK economy.
Mr Johnson - who was a key figure in the Leave campaign during the 2016 referendum and who took the UK out of the EU in January six months after becoming prime minister - said it was an "amazing moment" for the UK.
In his New Year message, the PM said the UK was now "free to do things differently, and if necessary better, than our friends in the EU".
Writing in the Daily Telegraph, he added that the combination of the Brexit deal and rollout of the Oxford vaccine means "we are creating the potential trampoline for the national bounceback".
Lord Frost, the UK's chief negotiator, tweeted that Britain had become a "fully independent country again" while veteran Conservative MP Sir Bill Cash said the outcome was a "victory for sovereignty and democracy".
But opponents of Brexit maintain the country will be worse off than it was while in the EU.
Scottish First Minister Nicola Sturgeon, whose ambition it is to take an independent Scotland back into the EU, tweeted: "Scotland will be back soon, Europe. Keep the light on."
Ireland's Foreign Minister Simon Coveney said it was "not something to celebrate" and the UK's relationship with Ireland will be different from now on, but "we wish them well".
French President Emmanuel Macron said the UK remained a "friend and ally".
What is changing?
The culmination of the Brexit process means major changes in different areas. These include:
- The free movement of people between the UK and EU countries has ended - and has been replaced in the UK by a "points-based" immigration system
- Anyone from the UK who wants to stay in most of the EU for more than 90 days in any 180-day period now needs a visa
- Duty-free shopping has returned, with people coming back to the UK from the EU able to bring up to 42 litres of beer, 18 litres of wine, four litres of spirits and 200 cigarettes without paying tax
- EU citizens wanting to move to the UK (except those from Ireland) face the same points-based system as people elsewhere in the world
- UK police have lost instant access to EU-wide databases on criminal records, fingerprints and wanted persons
- Traders in England, Scotland and Wales must complete more paperwork when dealing with EU countries
- British firms exporting goods to the continent will have to fill out customs declarations straight away.
While checks on goods entering Britain from the continent will be phased in over a six-month period up to July 2021, some new customs procedures have already come into force, on imports of alcohol, tobacco, chemicals and controlled drugs.
In other major breaks from the past, the European Court of Justice will cease to have any role in deciding disputes between the UK and EU.
And the UK will gradually be able to keep more of the fish caught in its own waters.
Unlike the rest of the UK, Northern Ireland will continue to follow many of the EU's rules, as its border with the Republic of Ireland remains all but invisible. The UK government said on Thursday online retailers in Britain will not have to make customs declarations when sending parcels to customers in Northern Ireland.
How prepared is the UK?
Intensive preparations have been taking place over the past two weeks to ready the UK for the coming changes, although concerns remain many small business are not ready.
The UK's Countdown Plan has involved operational testing of infrastructure at the border and close co-operation with France, Holland and Belgium.
A government spokesman said: "The border systems and infrastructure we need are in place, and we are ready for the UK's new start."
Vehicles trying to take goods across the channel without the correct documentation face being turned back while drivers of HGVs weighing more than 7.5 tonnes who do not have permits to enter Kent risk being fined.
Traffic volumes are expected to be lower than normal on 1 January due to the pandemic but are expected to pick up from Monday, when the new procedures and the UK's contingency measures are expected to be tested.
The government said 450 "Kent access" permits had been issued to HGV lorries intending to cross the channel at Dover on 1 January and hauliers arriving without them would be identified and subject to a £300 fine.
Meanwhile, the UK and Spain have reached an agreement meaning the border between Gibraltar and Spain will remain open.
Credit: The BBC