He left The Royal Ballet last year amid allegations of inappropriate behaviour.
A statement from his family said: “It is with great sadness that we announce the tragic, untimely death of our beloved Liam.
“At this difficult time for all of our family, we would ask that you respect our privacy to enable us to grieve our loss.”
Scarlett’s position with The Royal Ballet ended last year, when the Royal Opera House, which is home to the Royal Ballet Company, said that an independent investigation into Scarlett had concluded.
There “were no matters to pursue in relation to alleged contact with students of The Royal Ballet School”, it said.
Scarlett joined the Royal Ballet Company in 2006 and retired from dancing in 2012 to focus on choreography.
The artist-in-residence was investigated over claims of sexual misconduct involving students.
The allegations sent shockwaves through the ballet world, with Australia’s Queensland Ballet among those to cut ties with Scarlett.
The Royal Opera House previously said it was “made aware of allegations relating to Liam Scarlett” in August 2019.
“The individual was immediately suspended and an independent disciplinary investigation opened,” it said.
His works for The Royal Ballet include Despite, Vayamos al Diablo, Consolations And Liebestraum, Asphodel Meadows, Hansel And Gretel, Jubilee pas de deux, which was in celebration of the Queen’s Diamond Jubilee, and a new production of Swan Lake.
Performances of Scarlett’s production of Frankenstein were axed by the Royal Danish Theatre on Saturday over alleged misconduct towards several members of staff during rehearsals in 2018 and 2019, The Times reported.
A statement from the Royal Opera House on Twitter said: “We are deeply saddened to hear the news of Liam Scarlett’s death.
“Our thoughts are with his friends and family at this very sad time.”
Scarlett also worked with a host of other high-profile ballet companies, including the English National Ballet, the New York City Ballet, the American Ballet Theatre and the Norwegian National Ballet.