Mr Morgan's departure came hours after the Queen's Lancashire Regiment (QLR), the regiment at the centre of the abuse claims, demanded he say sorry.
A Royal Military Police inquiry concluded the photographs were "categorically" not taken in Iraq.
And Col David Black, a former QLR commanding officer, said: "It's time that the ego of one editor is measured against the life of the soldier."
Mr Morgan had earlier dismissed calls for him to resign saying: "All I want to say is we published the truth.
"We have revealed a can of worms. If the Government chooses to ignore that, it is entirely a matter for them."
However, the Mirror tonight said in a statement it had been the victim of a "calculated and malicious hoax".
"The Daily Mirror therefore apologises unreservedly for publishing the pictures and deeply regrets the reputational damage done to the QLR and the army in Iraq.
"The paper will continue to co-operate fully with the investigation.
"The Board of Trinity Mirror has decided that it would be inappropriate for Piers Morgan to continue in his role as editor of the Daily Mirror and he will therefore be stepping down with immediate effect."
Downing Street and the British Ministry of Defence tonight declined to comment but opposition parties and military chiefs were said to be privately celebrating Mr Morgan's departure.
Col Black last night spoke of "quiet satisfaction" at the departure of Mr Morgan.
He said: "I would like to see a full-scale apology on the front page of the Mirror apologising to the regiment for all the damage that has been done, to us in particular and to the army and the British reputation abroad as a whole. I might add that maybe with Piers Morgan's picture on it and not a fake one."
Col Black told BBC News 24: "But there is the wider question of course and that is the damage that has been caused out on the streets in Iraq and across the Arab world in general by the publication of these photographs. The damage there I believe will take a long, long time to repair if not being irreparable.
"We regard Piers Morgan as an obstacle to normalising relations with the Mirror. We now want the Mirror to come forward, offer an apology and co-operate fully with the investigation that is going on so we can get to the bottom of this particular nonsense.
He said of the Mirror's allegations: "I think they have just thrown up a smoke screen and wasted a lot of time, endangered a lot of people, angered and upset a lot of people. His removal hopefully will start to mend that rupture of relations."