"It is an action I am taking in order to redress the slurs, innuendo and hyperbole they have created around my standing in the entertainment industry and greater community", he said.
The initial article was based on an anonymous source who complained about an alleged incident that occurred during the production of William Shakespeare's King Lear, put on by the Sydney Theatre Company (STC) in 2015.
Rush said he would not be answering any further questions beyond his statement made to a packed room of journalists and flashing cameras at his lawyers office on Collins Street.
Mr Rush said Sydney's Daily Telegraph had caused "irreparable damage" to his reputation over reports it had published since 30 November.
Geoffrey Rush fronted a media conference in Melbourne Friday to announce that he has filed defamation proceedings against News Corp tabloid the Daily Telegraph after allegations of inappropriate behaviour were made against him.More news: Roper out as offensive coordinator for Gamecocks
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Mr Rush's lawyer said his client wanted to have this matter heard as quickly as possible and the actor would be seeking damages. He said he had not been informed of the nature of the complaint by the complainant or the theatre company, either at the time the complaint was made or since.
It comes after the Oscar victor stood down from his role as president of the Australian Academy of Cinema and Television Arts in light of the allegations.
A company spokesperson said the complainant requested the allegation be dealt with confidentially, and did not want Rush notified or involved in any investigation.
The situation is intolerable and I must now seek vindication of my good name through the courts.
One reporter asked if Rush had sought a retraction or apology from the Daily Telegraph. Share it on Facebook and you will help keep them up to date and help us earn the ad revenue we need to keep reporting. Thank you! Rush's film credits include Shine, The King's Speech and Pirates of the Caribbean.