Ms Miller’s lawyers said in court she believed the newspaper targeted medical records about her 2005 pregnancy, despite its publisher’s denials.
The actor, 39, has been paid a major financial settlement after taking legal action against News Group Newspapers.
Her lawyers told the court the payout is “tantamount” to an admission of illegal activity by the Sun.
The size of the payout is confidential – but it may be one of the largest settlements by Rupert Murdoch’s organisation to victims of phone hacking.
In a statement read on Ms Miller’s behalf at the High Court, she described how she felt the Sun “brutally took away her choice” when it allegedly leaked that she was pregnant.
Speaking outside court on Thursday, Ms Miller said the newspaper thought it was “above the law”.
She said the Sun’s actions “shattered me, damaged my reputation – at times beyond repair”, causing her to accuse family and friends of selling information “in a state of intense paranoia and fear”.
Ms Miller is one of the latest high-profile people to receive damages for historical phone hacking by tabloid reporters.
The NGN newspaper News of the World was closed down in 2011 after years of phone hacking came to light. Hundreds of celebrities, and members of the public, have since won compensation.