And in pro-EU Scotland, First Minister Nicola Sturgeon gave a clear sign of a looming battle ahead for a new vote on independence.
In a sign that the United Kingdom will break away from the European Union rules it inherited, Mr Johnson said: "We need the Brexit-given chance to turbocharge those sectors in which we excel, to do things differently and to do them better".
French President Emmanuel Macron, in a New Year's Eve broadcast, said Britain would remain a friend and an ally but Brexit was the product of "many lies and false promises".
Britain would work with partners around the world as it chairs the G7 club of nations and the UN's COP 26 climate change summit next year, the prime minister said.
He said the EU had provided the United Kingdom with a "safe European home" during the 1970s, but the country has now "changed out of all recognition" with global perspectives.
"This moment is finally upon us and now is the time to seize it", he said after Britain's Parliament approved a U.K. -EU trade deal overnight, the final formal hurdle on the U.K. side before departure.
There had been huge bottlenecks of traffic after France briefly closed the border in late December when a new coronavirus variant was found in Britain.
However, the British government, which is implementing a phased introduction of checks, expects next week to be the true test, once the quiet holiday period is over.
The Eurotunnel operator insisted today that Channel crossings "will work well" on New Year's Day after new Brexit trade rules come into force.
"It's a very sad day".
The end to European Union rules was a triumph for veteran Brexiteers such as populist politician Nigel Farage, a prominent voice in the 2016 referendum campaign to leave. "Well, they're not laughing now".
"If I understand it correctly, I am French".
Practical changes include how long Britons can visit their holiday homes on the continent, how to travel with pets, and an end to British involvement in an European Union student programme.
Opinion polls indicate that most Britons want to move on and are far more anxious about the worsening coronavirus pandemic, which has left more than 73,500 dead in Britain alone.
Special rules are now also in place for Gibraltar, a British overseas territory on the southern Spanish coast.
"If we don't celebrate in some way, we would just be crying", said Elaine Gilfillan, a teacher from Scotland who has lived in Spain for almost two decades. "It also provides a legal basis for arrangements for facilitating trade flows for importers and exporters", Norman said.
He added: "The common interests that Britain and the EU have now are the same interests that we had when the European project was formed in the early 1950s - trade and breaking down barriers to trade, so that Europeans and British people can get better quality consumer goods at lower prices".
United kingdom travellers are also confronted with a raft of new fees and charges, including increased journey insurance policy premiums to deal with the outgoing European Health Insurance Card (EHIC) plan, larger sized mobile phone expenses (even though some networks have pledged to keep on giving no cost roaming for the time now being), and far more charges and difficulties for those travelling with animals.