According to BrandRepublic, the deal is valued at £137.5 million.
2Waytraffic was set up in 2004 by former Endemol executives. The firm snapped up the rights to Who Wants To Be A Millionaire when it bought Celador International two years ago.
Sony Pictures Television – the branch of the company that handled the deal – already owns the rights to quiz shows such as Jeopardy and Wheel of Fortune.
Kees Abrahams, CEO of 2waytraffic, said: "The combination of 2waytraffic and Sony Pictures Entertainment Inc would allow us to further accelerate its growth strategy to become a leading producer and distributor of TV formats and interactive content across multiple platforms."
Sony is paying 2Waytraffic 108p a share, which adds up to an initial payment of £114.3m. The rest of the payment will be based on future performance. 2Waytraffic's directors have recommended that investors accept the offer.
In a trading statement issued today, 2Waytraffic said it expected to report pre-tax earnings of €29m for 2007.