He said he will leave the company in late 2011.
"With the Donmar's reputation in a particularly exciting place both at home and abroad, I feel now is the right moment to start a hand-over period to a new artistic director," Grandage said in a statement.
"It will enable someone to build on the success we have achieved over the last nine years and to look to the future with real confidence," he said. "I have spent nearly 15 years running organizations in the subsidized sector in Sheffield and London and the experience has been completely thrilling from start to finish. I am now keen to have a career that moves away from being in charge of a building in order to develop my work as a director in other ways. There are an enormous amount of people to thank for making the last few years the most exciting of my professional life and I look forward to engaging with each and every one of them in the months ahead."
Grandage's next production for the Donmar is "King Lear" followed by a new production of "Luisa Miller" in 2011.
Also next year, he is to make his debut at the Metropolitan Opera in New York with a new production of "Don Giovanni." In 2012, he is set to direct a production of "Evita" on Broadway.
His successor at the Donmar has not yet been named.