As deputy to the outgoing Carter, Richards was seen by many as favourite to become the regulator's second chief executive.
The process of appointing a successor to Carter began in June and a number of internal and external candidates were interviewed.
David Currie, Ofcom chairmanm said: "Ed has played a critically important role in the establishment of Ofcom. He has a profound understanding of the markets we regulate and is ideally placed to lead the organisation into the future."
Richards has been at the regulator since its inception in 2003 and was appointed its chief operating officer in July 2005.
Before joining Ofcom, he was the Prime Minister's senior policy adviser on media, telecoms, internet and e-government.
His role before that was controller of corporate strategy at the BBC, which was recently brought within Ofcom's remit for the first time.
While the BBC continues to answer to the government, Ofcom will evaluate jointly with the new BBC Trust whether the BBC's expansion into new services such as its iPlayer internet media service will have an acceptable impact on the communications market.
The other issues currently on Ofcom's plate include its ongoing consultation on advertising to children and the upcoming advertisement of a second national digital radio multiplex.
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