The 46-year-old, who later became Prime Minister David Cameron's communications chief, said he simply "rubber-stamped" the request by the royal editor of the Rupert Murdoch-owned tabloid.
Giving evidence in his trial on charges of paying public officials and phone hacking, Coulson repeatedly denied that he knew that journalists were illegally accessing celebrities' phones.
In particular, he denied an accusation from a former colleague that he had been played a hacked phone message left by actress Sienna Miller for James Bond star Daniel Craig.
The Old Bailey court in London was told about an email exchange in 2003 in which the News of the World's then Royal Editor Clive Goodman asked Coulson to sign off on a cash payment for a story.
Goodman said he wanted to buy a royal contacts book for £1,000 from a policeman assigned to the royal family, but warned that if they were caught the officer "could end up on criminal charges, as could we".
Coulson, who earlier told the court that Goodman was prone to creating "unnecessary drama", said he signed off on the cash.
"I didn't believe Clive was paying policemen, I still don't believe it. I think what I did was failed to address it properly with him," he told the jury.
"But I didn't (address it), I rubber-stamped it," he added.
Coulson resigned from the News of the World after Goodman and private detective Glenn Mulcaire were jailed for phone hacking in January 2007.
But he denies charges of conspiring to hack phones and paying public officials for stories.
A former colleague, Dan Evans, has already pleaded guilty to hacking and claims Coulson knew about the practice.
He said that in September 2005 he played Coulson a voicemail left by Miller on Craig's mobile phone that exposed their secret affair, which the then editor said was "brilliant".
Coulson was asked by his defence lawyer if such an incident took place, to which he replied: "No, it did not."
He said had no reason to believe the story of Craig and Miller came from phone hacking because his journalists had good contacts with celebrities.
He suggested it may have come from Miller's mother, adding: "People in and around celebrities, their relatives, their agents, their PRs, will talk to newspapers."
He noted that in the same week, he had been overseeing a "long, complicated" serialisation of British boxer Frank Bruno's biography, which "took up a lot of my time".
Source: AFP via I-Net Bridge
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