International Trade Secretary Liz Truss announced the deal was agreed in principle on Friday, and said it was the first to include dedicated chapters on digital trade and small businesses.
Exports to the three countries can be done using digital documents, contracts and signatures, the Department for International Trade said.
And it said the agreement significantly cuts tariffs as high as 277% for exporters to Norway of West Country Farmhouse Cheddar, Orkney Scottish Island Cheddar, Traditional Welsh Caerphilly, and Yorkshire Wensleydale cheese.
There are also tariff reductions and quotas on pork, poultry and other goods, and UK wines and spirits including Scotch Whisky will also now be recognised in Norway and Iceland.
While import tariffs on shrimps, prawns and haddock will be reduced, pushing down costs for UK fish processing and helping support some 18,000 jobs in that industry in Scotland, East Yorkshire and Northern Lincolnshire.
Ms Truss said: “Today’s deal will be a major boost for our trade with Norway, Iceland and Liechtenstein, growing an economic relationship already worth £21.6 billion, while supporting jobs and prosperity in all four nations at home.”
International trade minister Ranil Jayawardena added: “This deal shows that the United Kingdom will continue to be a trade partner of choice, as we set the global trade agenda in areas like e-commerce and climate change.”
The department said the deal also means British businesses can bid for more government contracts in partner countries worth some £200 million a year, and will allow caps on roaming charges and simpler visa processes for high-skilled professionals.
There is also an agreement where nurses, lawyers, vets and other professionals will be able to move to the three countries without having to requalify.
The department said the deal will allow caps on the charges mobile operators are allowed to charge each other for international mobile roaming, a world-first in an FTA, keeping costs low for holiday makers and business travellers.
Norway’s prime minister Erna Solberg said: “This agreement secures Norwegian jobs and facilitates economic growth, and it marks an important step forward in our relationship with the UK after Brexit.”
The Norwegian Government said the deal was one of the most comprehensive free trade agreements the country has ever negotiated but it was also recognised that it could not compare to previous arrangement when the UK was still in the EU.
A statement on the Norwegian Government website said: “Although the agreement ensures a predictable framework for Norwegian investors, exporters and services suppliers, it is not as comprehensive as the EEA-agreement.
“Prior to the UK’s exit from the EU, Norway enjoyed free movement of goods, services, capital and persons to the UK through the EEA-agreement.
“A free trade agreement will not provide similar access to the British market.
“Neither does the agreement remove a number of trade barriers that have been removed in the EEA Agreement.
“A free trade agreement does not provide for a common set of regulations and principles of mutual recognition, which ensure free movement, a cornerstone in the EEA agreement.”
Iceland’s minister of foreign affairs and international development cooperation, Gudlaugur Thor Thordarson, said: “I have placed great emphasis on ensuring a good future relationship with the UK after leaving the European Union and I am convinced that this agreement will strengthen the economic and friendly relations between Iceland and the UK in the future.”
Liechtenstein’s minister of foreign affairs Dominique Hasler added: “The agreement provides an excellent basis for continuing our close economic relationships and expanding them in the future.”