Coulson, former editor of the Rupert Murdoch-owned News of the World tabloid, is to be tried again on charges of conspiring to commit misconduct in a public office by paying a police officer for royal directories.
Jurors at London's Old Bailey last week convicted him of one charge of illegally accessing voicemails but failed to reach a verdict on the other charges.
His co-defendant, Rebekah Brooks, another former News of the World editor who went on to head the British arm of Murdoch's operation, was cleared of all charges.
Coulson was Cameron's director of communications between 2007 and 2011, a job he took after resigning from the News of the World.
He also quit Downing Street over the allegations and Cameron last week apologised for hiring him.
The phone-hacking trial was one of the most expensive in English legal history, spotlighting the close ties between the Murdoch empire and politicians and the no-holds-barred methods of Britain's tabloid press.
Clive Goodman, the News of the World's one-time royal editor, will also face a retrial on the same charges as Coulson.
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