Announcing a partnership between his Virgin Racing Formula E team and Citroen's DS brand, the billionaire also said he was willing to bet all new cars would be battery driven in 20 years' time.
"I think there's still going to be room for Formula One for another few more years," Branson told reporters ahead of the London ePrix in Battersea Park, south of the River Thames.
"But there will come a time when Formula E will overtake Formula One.
"I think four or five years from now you'll find Formula E overtaking Formula One as far as number of people," added Branson. "As time goes on, the clean energy-type of businesses are going to power ahead of other businesses."
Branson has experience of both series, with the 64-year-old sponsoring Formula One title-winners Brawn GP in 2009 and in 2010 entering with the Virgin Racing team which is now Manor Marussia.
His prediction is likely to be met with scorn in the Formula One community, however, with the glamour sport measuring a global television audience of hundreds of millions and top drivers ranking among the best-known and wealthiest sporting superstars.
Formula E cars make little noise and are far slower than Formula One and cannot currently complete a race distance due to the limitations of battery technology, with drivers having to change cars.
The arrival of DS, however, brings another major manufacturer into a series that is evolving and next year will allow teams to develop their own powertrains.
Renault and Audi are already involved while BMW electric vehicles are used as safety cars.
"The future is going to be fascinating and I'm taking my pills so I can live to see it," said Branson.
"I personally think things are going to move that rapidly now," he added. "What goes on in a petrol-driven engined is really complicated and antiquated and out of date and polluting."
Jean Todt, the president of the International Automobile Federation that governs both Formula One and Formula E as well as other conventional series, said, however, that comparisons should not be made between the series.
"I think it is a big mistake to compare," the Frenchman, who was in the audience to hear Branson, told Reuters. "It's two different things.
"It's like comparing London to a city on the beach...I really feel you need Formula One, which remains the pinnacle of motorsport, and you need Formula E, sportscar racing and rallying, touring cars and Formula Three."
(Editing by Ed Osmond)
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