Stevenson was found to have held what are being termed "inappropriate talks" with a potential partner for the BBC's digital curriculum and, after an internal investigation, the corporation has confirmed that this was "impermissable in the light of ongoing legal proceedings".
The corporation said on Monday that it had reached a deal with the 18 media and software firms, including RM and Reed Elsevier, which had been pressing for a judicial review into the funding of its digital arm.
In a statement, Stevenson said: "I made an error of judgement and, as a consequence, I have decided to leave the BBC, taking responsibility for what happened."
The case, launched in May 2002, was sparked by BBC plans to spend £150m of licence-fee money over five years on its online education activities, which would compete with commercial companies.
The government approved the plans in January, but with as many as 18 conditions imposed by the secretary of state for culture, media and sport Tessa Jowell. These conditions include an obligation to spend half of the content budget on private sector commissions.
"There is room for everyone. These conditions will prevent the BBC from dominating this market, but it's right that it should play an important role in a competitive and growing market for digital learning resources," Jowell said.
Greg Dyke, director-general of the BBC, said: "Michael has been criticised by the digital curriculum inquiry report and has taken the honourable decision to leave the BBC. I respect the way he has acted in taking this course of action."
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