Half of that investment will go directly towards the vehicle's creation, while the remaining £1 billion will fund battery technology that could be adapted for a variety of uses.
The announcement was sent out to Dyson employees on Tuesday afternoon.
"I wanted you to hear it directly from me: Dyson has begun work on a battery electric vehicle, due to be launched by 2020," Sir James said.
"We've started building an exceptional team that combines top Dyson engineers with talented individuals from the automotive industry. The team is already over 400 strong, and we are recruiting aggressively.
"I'm committed to investing £2 billion on this endeavour."
He said the project would "grow quickly" but did not release any further information, saying competition for new tech in the auto industry was "fierce".
"We must do everything we can to keep the specifics of our vehicle confidential."
The technology tycoon said that the idea had been brewing for decades amid concerns about global air pollution and vehicle emissions.