In a statement given today, Coulson said "continued coverage" of the phone-hacking scandal at the News of the World made it difficult for him to give the "110 per cent" needed for the job.
"I stand by what I've said about those events but when the spokesman needs a spokesman it's time to move on.
"I'll leave within the next few weeks and will do so wishing the Prime Minister, his family, and his brilliant and dedicated team the very best for what I'm sure will be a long and successful future in Government."
Coulson's resignation follows last week's news that the Crown Prosecution Service is to conduct a 'comprehensive assessment' of evidence held by the Metropolitan Police in relation to phone-hacking at the News of the World.
In January 2007, private investigator Glenn Mulcaire and royal correspondent for the News of the World Clive Goodman were convicted of conspiracy to intercept telephone calls while Coulson was editor. Coulson accepted responsibility for the practice and resigned from the newspaper, but has consistently denied any knowledge of phone hacking at the tabloid.
But the spotlight was back on the former editor last year following a report by the New York Times which carried allegations he had "actively encouraged" a reporter at the newspaper to hack into the voice messages of celebrities.
The report also contained accusations that Coulson has imposed a "hypercompetitive ethos" which encouraged reporters to do "whatever it takes" to get a story.
A recent Dispatches report followed included fresh allegations from a former colleague of Coulson’s, who claimed that the former editor had not only known about phone-hacking at the tabloid but had asked recordings to be played to him.
In a statement today, David Cameron, who refused to comment on resignation rumours during an interview on Monday's Today programme, said he understood why the pressures on Coulson and his family made him feel "compelled" to quit.
"Andy has told me that the focus on him was impeding his ability to do his job and was starting to prove a distraction for the government.
"During his time working for me, Andy has carried out his role with complete professionalism. He has been a brilliant member of my team and has thrown himself at the job with skill and dedication. He can be extremely proud of the role he has played, including for the last eight months in Government.
"I wish Andy all the very best for his future, which I am certain will be a successful one."
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