Rush denied the allegations in a statement to the Daily Telegraph issued through his lawyers.
The newspaper article last month said an Australian theater company had received a complaint about "inappropriate behavior" following the production of King Lear two years ago in which Rush was the star. The company has released no details of the complaint other than it alleged "inappropriate behaviour " while Rush was an employee and was not raised until after he had left.
"Today I have filed defamation proceedings against The Daily Telegraph in the Federal Court of Australia", the Academy Award victor said.
The newspaper, owned by News Corp Australia, ran allegations against Rush that he called hyperbolic and untrue.
"The Daily Telegraph has made false, pejorative and demeaning claims - splattering them with unrelenting bombast on their front pages".
The allegations have come after a string of high profile sexual abuse complaints against entertainment industry heavyweights such as Harvey Weinstien, Kevin Spacey and Matt Lauer.
Rush's lawyer Nicholas Pullen said Rush was unable to answer questions about the case.
"The situation is intolerable and I must now seek vindication of my good name through the courts", Mr Rush added.
Last week, Rush voluntarily stepped down as president of the Australian Academy of Cinema and Television until the matter is resolved.
"We will defend our position in court".
The Daily Telegraph reported the matter would go before the Federal Court in Sydney on February 8.
When asked about the claims being leveled against Rush, Australian actress Rachel Griffiths said the actor "is not Harvey Weinstein" - referencing the Hollywood mogul who faces multiple allegations of sexual misconduct.
Mr Rush is one of Australia's most celebrated actors, having starred in films including Shine, Elizabeth and The King's Speech.
The publisher has since said it would appeal the payout as the "unprecedented" amount had major implications for the media industry.