Sir James gave no details away on what the car will look like, saying only that it would be a major departure from existing cars.
"There's no point in doing one that's like everybody else's. You'll have to wait and see, we're trying to be radical," he said.
Dyson is not working with any existing manufacturers on the project, planning to build the car from scratch.
It is going public with the plans since it will now have to start talking to various governments about production and testing of the vehicle, as well as needing to hire car experts.
Sir James said it was investing £1b (NZ$1.8b) in the car project and another £1b (NZ$1.8b) in battery technology to support it. Dyson has two competing teams working on "solid state" batteries, which are seen as safer and denser than existing lithium-ion batteries.
The company currently has a team of 400 staff working on the vehicle, but Sir James said the company's 4,000 staff in the UK could eventually "double" due to the project. He said the first vehicle would be at the pricey, "high-tech" end of the market, but that there would eventually be a range of vehicles.
Sir James said the first vehicle would employ basic self-driving features but that the first car would not be fully self-driving. In July, the Government announced that it would ban sales of petrol and diesel cars by 2040.
Sir James said he had tried in vain to get car and lorry makers to fit emission-cutting "cyclonic exhausts" onto Diesel engines in the 1990s in vain, and being overlooked had forced him to take matters into his own hands.
"We're not a Johnny come lately, it's been an ambition since 1998 when we were rejected by the industry. [Since then] it's been my vision to come out with an all electric car, it wasn't a fashionable thought [then]."
He hinted that prospective buyers may be able to put deposits down on vehicles before 2020.
Sir James said the company had not decided where the vehicle would be manufactured but that it would be near to where its customers are, saying the UK and Asia were among the frontrunners.