In a personal statement issued by number 10 Mr Coulson said: “Unfortunately continued coverage of events connected to my old job at the News of the World has made it difficult for me to give the 110 per cent needed in this role.”
Mr Coulson resigned as editor of the News of the World in 2007 after the paper’s former royal editor Clive Goodman and private investigator Glenn Mulcaire were jailed for phone hacking.
Although he took responsibility, he has always denied knowledge of the illegal activities.
But a number of famous figures are still taking civil legal action against the newspaper and documents disclosed in those cases have led to new developments.
The timing of the resignation sparked claims that the government was “burying bad news” coming as former prime minister Tony Blair was giving evidence to the Iraq inquiry and with the spotlight still on shadow chancellor Alan Johnson’s resignation.
“This is the second job that Andy Coulson has resigned from for something he claims to know nothing about,” he said.
“His departure creates serious questions over the Prime Minister’s judgement and points to the need for a deeper investigation into the affairs of Rupert Murdoch’s News Corp.
“It’s a mark of the man that he would sneak out a statement on a Friday morning on a busy news day.”
In the Commons former minister Denis MacShane demanded that Mr Cameron come to the chamber to make a statement on Mr Coulson’s resignation.
In a point of order he said: “I believe it would be appropriate for the Prime Minister to come to the Commons to explain why this is happening and give the public the full details here in the House of Commons, rather than bury this news on a day when, frankly, there’s an awful lot of other news taking place.”
But Deputy Speaker Lindsay Hoyle said it was “nothing to do with this House” if a member of the Prime Minister’s staff had resigned.