Nadia Fall is taking over at the Young Vic Theatre after current boss Kwame Kwei-Armah announced he was leaving.
Fall, who has run Stratford East for seven years, will take the top job at the theatre in Waterloo in January.
She said: “The Young Vic was first built as a pop-up theatre for a younger, bolder generation of artists and audiences. Today it is a celebrated cornerstone of London theatre but that mischievous spirit of a makeshift, anti-establishment theatre still courses through its veins, and I find that incredibly compelling.
“The Young Vic is not afraid to ask the difficult questions, and it’s particularly exciting to me that its audiences have an appetite for that provocation.”
Fall, who grew up in south London and the Middle East, said the theatre “holds hands with its local community” while also “looking out towards the rest of the world”.
She said: “It’s exactly who we are in London - both local and international.”
Kwei-Armah is stepping down in September after his final production, A Face in the Crowd, opens at the theatre.
Fall has also worked at the National Theatre and has just made her first feature film Brides.
Her previous work includes a revival of Equus which moved to the West End and working with names including Lenny Henry and Michaela Coel.
Kwei-Armah congratulated her on the role, saying: “Nadia will get to work with some of the most dedicated and skilled theatre people in our sector, and they will get to work with a fearless artistic leader.”