In this role Kumar, who was previously head of BBC HD, will report to Erik Huggers, the recently appointed director of the BBC's Future Media & Technology department, a release from the BBC said.
Kumar will lead a new bbc.co.uk board consisting of executives from across the organisation and lead the editorial development of the site, as part of her new responsibilities.
The controller position was created following the BBC Trust's review off bbc.co.uk in May, which found that the corporation had overspent by £36 million on the website.
The review said the site's management structure was the main reason for the overspend and called for the BBC Executive to submit plans for a new management system.
Speaking about her appointment, Huggers said her 'strong editorial background' would help the website 'build on the strengths identified by the Trust in their recent review'.
In her previous role, Kumar launched the BBC's HD service in December last year.
Tony Ageh, the BBC's controller, internet, is also set to take up an as yet unspecified 'senior role' within the corporation, the BBC announced.
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