Sir James bought the luxurious flat – said to be Singapore’s largest – last year after announcing he was moving Dyson’s headquarters to the city state.
The company is best known for vacuum cleaners, air purifiers and hair dryers.
Dyson also considered building an electric car factory in Singapore, before pulling the plug over concerns about the car’s commercial viability.
Sir James, who topped the Sunday Times Rich List this year, was an advocate for Brexit.
He was accused of hypocrisy when he first announced the move to Singapore in January last year, but the company has long maintained the move had nothing to do with Brexit or tax.
Singapore’s largest penthouse occupies the top three levels of the 64-storey Guoco Tower, in the city’s Tanjong Pagar neighbourhood.
Marketing materials advertised the five-bedroom property as the largest “non-landed residence” in Singapore.
The penthouse offers views of Singapore’s harbour and financial district, and comes with its own swimming pool, jacuzzi room and bar facilities.
The reported buyer is Indonesian-born tycoon Leo Koguan, who is the co-founder and chairman of IT provider SHI International.