Born in 1990, Essiedu grew up in East London with his mother, who was a fashion and design Teacher. His family comes from Ghana, where he has a half-brother and half-sister. He won a scholarship to Forest School, Walthamstow and despite being active in Sports teams and theatrical productions his ambition as he grew older was to become a Doctor. Essiedu became more involved with Shakespeare when he was accepted into the Guildhall School of Music and Drama. He takes inspiration from his favourite actors: Mark Rylance, Chiwetel Ejiofor, Simon Russell Beale, David Thewlis, and Gary Oldman.

Essiedu joined the Royal Shakespeare Company in 2012 to play Fenton in Phillip Breen's production of The Merry Wives of Windsor. Afterwards, he went to the National Theatre, playing Burgundy and understudying Edmund in Sam Mendes’ production of King Lear. When Sam Troughton lost his voice during a performance, Essiedu, then his understudy, stepped in and played the role to critical acclaim. He has acted in Outside on the Street (Pleasance Theatre), Black Jesus (Finborough Theatre), Romeo and Juliet (Tobacco Factory), You For Me For You (Royal Court), and most recently the title role in Hamlet and Edmund in King Lear, both at the (Royal Shakespeare Company). The judges described his Hamlet as one the audience listened to "completely still", and they noted that as an actor he could turn on a sixpence – sweet, playful and flirtatious one minute, and fiercely intelligent the next. "Like all great actors," a judge noted, he "made all the lines his own". His Edmund in King Lear was noted for his chilling contempt and cynicism.