The billionaire, who was a prominent backer of Brexit, told the BBC he was "enormously optimistic" about trading with the rest of the world.
His comments came as his engineering firm Dyson reported a 41% increase in profits to £631m.
The popularity of its vacuum cleaners in fast-growing Asian markets was a major reason for the rise.
The company said sales of its products increased by 45% to £2.5bn, helped by growth of 244% in China, 266% in Indonesia and 200% in the Philippines.
The success of new product lines such as hair dryers also fuelled growth.
On Wednesday, Prime Minister Theresa May is due to start the process of the UK leaving the EU.
In an interview with the BBC, Sir James said: "Europe's only 15% of the global market and the really fast-expanding markets are in the Far East.
"I'm enormously optimistic because looking outwards to the rest of the world is very, very important because that's the fast-growing bit."
Sir James Dyson is the poster child for the kind of global-facing confidence the government is keen to harness in a week that it signals the beginning of the end of the UK's membership of the EU.
The entrepreneur has been a prominent supporter of Brexit and remains clear that British business success lies beyond Europe.
He is putting his money where his mouth is - investing £2.5bn, expanding his Wiltshire base by buying 500 acres of old airfield in Hullavington and hoping to double his 3,500 workforce in the next four years.
Critics, though, say that while he designs products in the UK, he manufactures them in the Far East and so his export arrangements may not be subject to the same Brexit uncertainty as for those manufacturing in the UK.
Sir James said it would be possible to remain close to Europe after Brexit, while also forging closer ties with Commonwealth countries.
"I'm a patriot, which is why I'm rather keen on re-connecting with the Commonwealth," he said.
And he rejected the suggestion EU staff could be forced to leave the UK - saying it was "absolute nonsense to suggest countries are going to chuck out foreign citizens".
The entrepreneur, who has criticised the lack of British engineers, also defended his decision to have major operations in Asia, saying the firm's intellectual property and profits were still in the UK.
"I'm resident in England, we pay all our tax here," he added.
Dyson designs many of its products in the UK, but largely manufactures them in Asia.  It has tripled its team in China and recently opened a new £330m research centre in Singapore.
The firm is also opening a new multimillion-pound research centre in Wiltshire, England and a university at its existing Malmesbury campus in the Cotswolds.
Sir James Dyson has said UK business success lies beyond Europe because that is where the fastest growth lies.