Mr Stretton's sudden departure one year into a three-year contract, the day after a board meeting, follows disagreements with dancers over his management style.
Recent reports that dancers were "infuriated" by the Australian's methods were followed by a series of negotiations to resolve "a number of casting and management issues".
Mr Stretton described his time at the company, based at the Royal Opera House in Covent Garden, London, as "enormously challenging and rewarding both professional and personally".
"Even though I have enormous respect for the great heritage of this company, my interest lies primarily in developing the future of ballet, and that is what I want to spend my time doing," he said.
"I have discussed this matter with the Royal Opera House board, and I feel that I am choosing the most appropriate course of action."
Mr Stretton, 50, is a former director of the Australian Ballet and assistant director of the American Ballet Theatre.
His reign at the Royal Ballet was criticised for an unimaginative repertoire in which he has failed to stage as many new productions as expected.
There were complaints from dancers about changes to schedules and that he kept them in the dark about who would appear in which performances.
The Independent newspaper reported that only two of 22 recent shows ended up going ahead with the cast that had originally been announced.
The company's Jubilee gala for the Queen was widely drubbed by critics, one of whom described it as "unstylish and incompetent".
Critics also complained of too few English ballets, too few world premières and too many dull modern works.
A series of negotiations between dancers and the Royal Opera House executive director Tony Hall was only completed in September, but were said to have been going in the right direction.
In the end Mr Stretton seems to have lost the confidence of the management at the Royal Opera House as well, said media correspondent Nick Higham.
One source said the reasons for his departure included his style of management and his failure to build a satisfactory relationship with members of the company.
Sir Colin Southgate, chairman of the Royal Opera House, said he accepted Mr Stretton's resignation "with deep regret".
Leaving immediately
"I would like to thank him for his work over the last 12 months and in the period building up to his arrival here," he said.
"The Royal Ballet has been introduced to some new and interesting works under Ross's stewardship."
Founded in 1931 by Ninette de Valois, the Royal Ballet has developed into one of the world's leading companies.
Originally based at Sadler's Wells Theatre in Islington, it moved to the Royal Opera House in 1946 and became the Royal Ballet 10 years later.
Its cast of principal dancers includes Darcey Bussell, Romanian starlet Alina Cojocaru and French lead Zenaida Yanowsky.
Mr Stretton will leave immediately and assistant director Monica Mason will fill his role until a new director is found.
After a turbulent time in the 1990s Covent Garden has had a smoother ride lately, added Mr Higham.
The Opera House would rather Mr Stretton's departure was seen as firm action by a strong management, rather than as evidence that Covent Garden's old problems may be about to return, he said.