The Football League chairman Keith Harris is also understood to have stepped down. Earlier today, in an interview on Radio 4, Harris had said he would be willing to take on the chief executive role in the short term, should the members ask him to do so.
The league held a board meeting this morning, after growing pressure from members for Burns to go. Burns said: "I have, by mutual agreement, terminated my employment with the Football League."
Last week, the High Court ruled that Carlton and Granada would not have to pay the Football League £178.5m relating to football rights bought by ITV Digital before it collapsed this year. The Football League could now sue its solicitors for failing to get a guarantee over the payment from the owners of ITV Digital.
The case has left the league with legal bills of around £1m, at a time when many of its members are facing financial ruin.
In Burns' statement, he said: "Throughout my 21 months as chief executive, I have worked tirelessly to improve the league's position commercially and politically, to raise and enhance its public image and to ensure fair media representation.
"A great deal of progress has been made and I leave behind a talented and dynamic executive team capable of taking the league forward well into the future.
"When I joined the league, the ITV Digital contract -- the subject of the recent High Court legal action -- was already in place, having been finalised by the previous administration."
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