Frank became known the world over through the posthumous publication of her journal.
Frank was 13 when she and her Jewish family hid in a secret annex of her father's Amsterdam office building in Nazi-occupied Holland during World War II. The family hid for two years before they were discovered. Frank died of typhus in the Bergen-Belsen concentration camp in 1945.
Based on her diary and with actress Ellie Kendrick playing the title role, the miniseries will air over five consecutive nights on BBC One early next year.
The BBC said the drama would "bring Anne alive to viewers of all generations."
Executive Producer John Smithson said it was a "portrayal of a family living through the most horrifying times.
"We want audiences to identify with all the characters in the story -- particularly Anne who, as a bright, funny, energetic teenager, still seems entirely modern today."
The drama will also star Iain Glen and Tamsin Greig as Frank's parents.