The executive, who is paid £212,100 a year, said it was an "opportunity" he could not turn down. The decision to move the channel online was announced last month and is expected to save £50 million a year.
Mr Bennett, 39, who joined the BBC in 2011, said: "I leave BBC Three on top form, with its highest ever viewing share and six nominations at this year's Baftas."
He will become director of Sky Atlantic, the pay channel home to big US dramas including Game of Thrones and Mad Men.
Mr Bennett, who will join Sky in August, also worked for 12 years at ITV where he commissioned hit shows including The Only Way is Essex.
Sky's director of entertainment channels Stuart Murphy, also a previous BBC Three controller, said: "Having admired his work for years, it's great to now have him on the same team. Zai's desire to welcome and support creative risk is a perfect fit for Sky."