Burke, former director of value-added services at BT Retail, joined the newly created division of BT Entertainment as CEO in November 2004.
The company told the Financial Times that he had left by "mutual consent to pursue other interests" and that his departure had been "amicable".
However, reports suggest that there was unrest within the group between Burke and Ian Livingston, chief executive of the retail division, over his plans to build up the entertainment business.
A spokesperson at BT denied the reports of and said: "Reports that there is unrest are completely untrue, it is completely amicable."
Burke was the driving force behind the service, which distributes on-demand music, gaming, TV and movies via broadband.
Last month, BT announced its TV service would be called BT Vision and said that it plans to launch the service nationwide in the autumn.
The proposed service is a combination of Freeview's free-to-air digital terrestrial channels and access to premium content, including a video-on-demand film library and channels such as the Cartoon Network and National Geographic.
Burke has previously been CEO of eVerger, the media venture capital fund, and prior to that chief operating officer of eVentures, the internet capital fund owned by News Corporation and Softbank.
He was also founder and CEO of LineOne, the UK internet service provider and established News International's initial internet presence in 1995.
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