Effectively, Kumar replaces Tony Ageh who was the BBC's controller, internet. The BBC said Ageh is moving to another senior role within the BBC, which will be announced shortly.
Kumar will lead the overall strategic and editorial development of bbc.co.uk and will chair a new bbc.co.uk board, which will bring together executives from across the BBC.
In partnership with Kerstin Mogull, chief operating officer for the future media and technology, Kumar will be accountable for the performance of the service to the BBC Trust.
She takes up her position immediately and will report to Erik Huggers the BBC's director of future media and technology.
As head of BBC HD, Kumar was responsible for launching the UK's first high definition public service free-to-air channel in December 2007.
Prior to this Seetha was executive editor of the award- winning Africa Lives, head of lifeskills for television and creative director for crime and health documentaries.
Huggers said: "Seetha has proven experience working collaboratively to deliver major projects which exploit the scale of the BBC and is ideally suited to overseeing the one service where audiences can experience the BBC in its totality -- it's the BBC on the web."
Her appointment follows that of Mogull who was named to the newly-created role of chief operating officer, FM&T, earlier this week.
Mogull's role is to focus on the management and governance of the division, its partnership with other BBC divisions -- vision, audio & music and Journalism -- and its relationship with the BBC Trust.
She was previously deputy director, policy & strategy where she played a key role in driving the BBC's strategy for content across all media platforms.
Prior to that, she was controller for the strategy group, where she was responsible for some of initiatives such as delivering creative future.