Coulson, 46, who previously served as communications chief of Cameron, was handed down the sentence at the Old Bailey court in London alongside three other former News of The World colleagues.
Former chief reporter Neville Thurlbeck, 52, and ex-news editor Greg Miskiw, 64, were jailed for six months.
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Members of the British royal family, celebrities and crime victims were among some of the victims of hacking at the now defunct News of the World (NoW).
Coulson, one of the seven defendants in the high-profile phone-hacking trial, was found guilty of plotting to intercept voicemails between 2000 and 2006 for stories in the tabloid following a marathon eight-month trial.
The maximum sentence in such a case is two years.
Former News International chief Rebekah Brooks and four others were cleared of all charges on June 24.
Coulson and the newspaper's former royal editor, Clive Goodman, also face a retrial on a charge of buying royal telephone directories from police officers after the jury failed to reach a verdict on these charges.
Judge John Saunders said: "Mr Coulson on the jury's verdict has to take the major blame for the phone hacking at the News of the World."
"He knew about it and encouraged it when he should have stopped it."
Following Coulson's conviction, Cameron was forced to make an embarrassing apology for hiring him and said he would not have done so had he known about his actions at the 168-year-old tabloid. The publication was shut down in disgrace in July 2011 amid a public outcry.
Coulson was appointed Conservative Party director of communications in July 2007, six months after he stepped down as NoW editor.
After Cameron became Prime Minister in 2010, Coulson was appointed his director of communications.
Coulson maintained that he knew nothing about hacking at the paper while he was editor but was forced to quit Downing Street in 2011 after allegations about it intensified.
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