Assistant coach Terry Venables has also lost his job in what the FA said was a unanimous decision by its board.
The FA brought a swift end to McClaren's 18-month reign as England's head coach at an emergency meeting.
McClaren's position had become untenable after the 3-2 defeat to Croatia on Wednesday.
FA chairman Geoff Thompson said: "Like every England fan, we are all bitterly disappointed that we have failed to qualify for Euro 2008, and I know Steve feels that disappointment more than anyone.
"Of course we have no divine right to play in major tournaments, but it is quite right that qualification is expected.
"I would like to thank Steve for the work he has done since taking on the position last summer. His commitment to the job could not be questioned and I wish him the best for the future.
"The recruitment process for the new coach begins now and we will do everything to get the right man for the job."
The FA has plenty of time to search for a replacement with the next scheduled fixture a friendly in France at the end of March.
FA chief executive Brian Barwick confirmed that nationality would not be an issue as he leads the search to find McClaren's successor.
Barwick also admitted that errors were made in the selection process when McClaren was appointed in July 2006.