She had to be taken away by the court matron after the verdicts were read out, following a seven month trial.
But former No 10 spin doctor Coulson was found guilty of plotting to hack phones while he was editor of the News of the World.
Coulson, who was forced to resign as Prime Minister David Cameron's director of communications over the scandal, now faces the possibility of jail following the high-profile trial at the Old Bailey.
But the jury of eight women and three men cleared ex-News International chief executive Rebekah Brooks of all charges.
Rebekah Brooks has been cleared of all charges
Brooks was overcome by emotion on hearing the verdicts and was taken away by the court matron.
Retired managing editor Stuart Kuttner was also cleared of being part of a conspiracy dating back to 2000 and spanning six years.
Brooks's former personal assistant Cheryl Carter was cleared of conspiracy to pervert the course of justice. Brooks's husband Charlie and NI director of security Mark Hanna were also cleared of perverting the course of justice.
But the jury, which has been considering verdicts since June 11, is still considering further charges against Coulson and Clive Goodman, former royal editor at the NoTW, of conspiring to commit misconduct in a public office by paying police officers for two royal directories.
The partial verdicts were delivered on the jury's eighth day of deliberations and the 138th day of the trial.
Coulson was convicted of phone hacking
Ex-No 10 spin doctor Coulson, 46, of Charing, Kent; had denied all the charges as had Goodman, 56, of Addlestone, Surrey.
Brooks, 46, was cleared of hacking, misconduct in a public office for allegedly signing off payments to a Sun journalist's "number one military contact" between 2004 and 2012, conspiracy to pervert the course of justice and perverting the course of justice.
Carter, 50, of Chelmsford, Essex, was cleared of perverting the course of justice by removing seven boxes from the NI archive just days before she was arrested in 2011.
Racehorse trainer Charlie Brooks, 52, of Churchill, Oxfordshire, and Hanna, 51, were cleared of perverting the course of justice around the time of police searches in July 2011.
Mrs Brooks, dressed in a white blouse, appeared to hold the hand of Ms Carter as she was cleared.
The pair looked at each other supportingly in the dock after the not guilty verdict against Ms Carter was given to the court.
On Mrs Brooks other side was her husband Charlie, who stood with his hands folded in front of him as he was cleared.
His wife brushed him comfortingly as the verdict was given, while he stood staring straight ahead.
Coulson, dressed in a dark suit, showed no immediate reaction to the guilty verdict, standing with his hands behind his back and clenching his jaw while looking forward.
A few moments later he took a deep breath in and out.
George Osborne has come under fire for recruiting Coulson to head up the Tory media operation within months of resigning as editor of the NoTW in January 2007.
A spokesman for the Prime Minister said Cameron "entirely" stood by his words to parliament in July 2011, when he told MPs: "I have said very clearly that if it turns out Andy Coulson knew about the hacking at the News of the World he will not only have lied to me but he will have lied to the police, to a select committee, to the Press Complaints Commission and, of course, perjured himself in a court of law."
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