Dominic Elliott, 23, died at Scarborough General Hospital at around 6am on Sunday morning.
The studio assistant had sat for David Hockney on more than one occasion at his studio in Bridlington, East Yorkshire.
Humberside Police said that they were contacted after Mr Elliott had been taken to the hospital by a friend in a serious condition, but that there were no immediate signs of violence at the scene.
A post mortem examination is due to take place on Tuesday.
“The circumstances of the man’s death are not clear and officers are currently undertaking inquiries to establish events leading to his death,” said a police statement.
Tributes were paid to Mr Elliott by members of the rugby club where he played in the seaside town. Bridlington Rugby Club chairman Gordon Morrice told a local newspaper that he was a “popular lad” with many friends at the club.
Mr Hockney, 75, is one of the most famous British artists of his generation and was celebrated at the Royal Academy of Arts last year with an exhibition of his large scale landscapes, called A Bigger Picture.
The blinds were drawn at Mr Hockney’s large, detached house in Bridlington near the sea on Monday morning and no-one was available for comment.
The Bradford-born artist is famous for artworks such as A Bigger Splash, a vivid depiction of a Los Angeles swimming pool, and the portrait Mr And Mrs Clark And Percy.