McQueen, who grew up in west London, is widely expected to pick up an Oscar nomination for best director for his latest film 12 Years A Slave.
Corporation bosses are staying tight-lipped about the planned series which has been described as "a major drama" and is believed to be set in the capital and stretch from the late 1960s to the present day.
BBC drama controller Ben Stephenson said: "It is too early to announce the details, but it is incredibly exciting to be working with the hugely talented British director who has rapidly become one of the finest directors in the world."
McQueen, who now lives in Amsterdam, first found fame as a video artist winning the Turner Prize in 2006.
His mainstream movie career began with 2006's Hunger about the Northern Irish hunger strikers.