The theatre's Facebook page says he made a great contribution to the theatre scene in New Zealand and will be sorely missed.
Arts, Culture and Heritage Minister Christopher Finlayson this afternoon expressed his sadness at Tilly's death.
"Grant had been unwell for some time and his passing is very sad,'' said Mr Finlayson.
"It is impossible in a press release to list all his achievements in the theatre. He was one of a small group of people who formed Circa Theatre in 1976 and built it into its pre-eminent position today,'' he said in a statement.
"My thoughts are with his family, his old friends at Circa and the theatre community.''