The deal was secured on Christmas Eve, a week before current trading arrangements expire.
A UK source said the deal delivered “everything that the British public was promised during the 2016 referendum”.
Prime Minister Boris Johnson and European Commission president Ursula von der Leyen were in close contact over recent days to help get the deal over the line.
But negotiations led by the EU’s Michel Barnier and the UK’s Lord Frost continued throughout the day as final details were hammered out.
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European Commission President Ursula von der Leyen said: “First of all, competition in our single market will be fair and remain so.
“The EU rules and standards will be respected. We have effective tools to react if fair competition is distorted and impacts our trade.
“Secondly, we will continue cooperating with the UK in all areas of mutual interest, for example in the field of climate change, energy, security and transport.
“Together, we still achieve more than we do apart.
“And thirdly we have secured five and a half years of predictability for our fishing communities.”
James Ramsbotham, chief executive, North East England Chamber of Commerce said: “The last four and a half years have been a nightmare of uncertainty for so many of our North East businesses. While we welcome this step towards establishing a new relationship with the EU it is important to remember this is not the end, but the beginning.
“Businesses still have no clarity on a wide range of important trading issues at a time when their attention is also focused on the increasing challenges arising from Covid.
“We have had two years to plan a seamless transition but now just days to adapt to the most significant changes in our trading relationship with the EU in over 40 years. This deal leaves businesses with precious little time to adjust.
“Many companies also remain nervous about how to maximise their potential when trading with the EU going forward. This is of particular importance to our region with Europe being our largest marketplace.
“We need to see temporary measures, exemptions and support to minimise disruption as far as possible. This should not be the end of the conversation between UK and EU, but the start of an ongoing process that continually seeks to improve trading conditions.”
David Frost, the UK’s lead negotiator, tweeted: “I’m very pleased and proud to have led a great UK team to secure today’s excellent deal with the EU.
“Both sides worked tirelessly day after day in challenging conditions to get the biggest & broadest trade deal in the world, in record time. Thank you all who made it happen.
“Today’s agreement does more than just deliver a zero tariffs deal. It covers areas such as services, aviation, road transport, social security, health, fisheries, and, crucially, law enforcement. And it allows us to participate in the Horizon scientific research programme.
“It also restores Britain’s sovereignty in full. EU law ceases to apply; the jurisdiction of the European Court of Justice ends; there is no alignment with EU rules; and our Parliament sets all laws for our country once again.
“Our country begins a new journey as a fully independent country once again on 1 January. Our future and our prosperity are in our hands. I am confident we will thrive and succeed.”
The EU’s chief negotiator outlined some of the ways the UK and the EU will work together.
Michel Barnier told a press conference: “We have achieved reciprocal access to waters and to resources, and with the new distribution of fishing quotas and fishing opportunities which has been directly agreed, as is only natural, between the president of the European Commission Ursula von der Leyen and Prime Minister Johnson, with taking account of Britain’s new status as an independent coastal state, that is a state which will no longer be part of the common fisheries policy just a few days from now.
“This agreement will require efforts. I know the European Union will support its fishermen and women, will accompany them, and that is our commitment.”
He continued: “Our partnership also includes co-operation in the field of research and innovation, nuclear safety, space, in the framework of EU programmes.
“In this field, our partnership will also include a non-discrimination policy concerning EU citizens which will apply to visas, to services, and to co-ordinating social security.”