The 67-year-old Australian had sued Sydney's The Daily Telegraph's publisher and journalist Jonathon Moran in the Federal Court over two stories and a poster published in late 2017.
Justice Michael Wigney found in April the publisher, News Corp.-owned Nationwide News, and Moran were reckless regarding the truth when they reported Rush had been accused of inappropriate behavior by actress Eryn Jean Norvill. She played the daughter of Rush's character in a Sydney theater production of "King Lear" in 2015 and 2016.
The judge found a poster and two articles contained several defamatory meanings, including that Rush was a pervert and a sexual predator, but the publisher had not proven the meanings were true.
Wigney at the time awarded Rush AU$850,000 in damages plus AU$42,302 interest for non-economic loss. But he wanted to consider further special damages, including loss of earnings.
Following an agreement between the parties, the judge on Thursday awarded Rush a further AU$1.98 million for past and future economic loss.
The publisher and journalist are appealing the verdict.
Rush's lawyer, Sue Chrysanthou, said Rush had offered in early 2018 to settle in exchange for an apology and AU$50,000 plus costs, but Nationwide News did not respond.
Comic actress Rebel Wilson in 2017 had previously won an Australian record AU$4.7 million damages in a defamation case against a magazine publisher. But the damages were reduced by 90% on appeal.
"Orange Is the New Black" actress Yael Stone was revealed two weeks ago as the potential witness who Wigney refused to allow to testify in Rush's defamation suit.
Nationwide News lost a mid-trial bid last November to amend its defense based on Stone's evidence.
Wigney said the proposed amendment raised new allegations concerning Rush's conduct and would delay court proceedings and cause him "manifest and palpable" prejudice. The trial by then had run for 12 days and ended three days later.
The judge prohibited Stone from being publicly identified. The Netflix series actress was described in the media as "Witness X."
Stone told The New York Times in December that Rush engaged in sexually inappropriate behavior when they starred in "The Diary of a Madman" on a Sydney stage in 2010.
She said Rush danced naked in front of her in their dressing room, used a mirror to watch her while she showered and sent her occasionally erotic texts.
Rush said in a statement the allegations "are incorrect and in some instances have been taken completely out of context."
"However, clearly Yael has been upset on occasion by the spirited enthusiasm I generally bring to my work. I sincerely and deeply regret if I have caused her any distress. This, most certainly, has never been my intention," Rush said at the time.
Rush won the best actor Oscar in 1996 for his portrayal of pianist David Helfgott in "Shine" and was nominated for roles in "Shakespeare In Love," "'Quills" and "The King's Speech." He is also famed for his portrayal of Captain Barbossa in the "Pirates of the Caribbean" films.
He received Australia's highest civilian honor in 2014, the Companion of the Order of Australia, for service to the arts.
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