Okonkwo was one of ten actors selected from twelve thousand applicants for the BBC Talent Scheme in 2001, leading to his first professional acting role in Holby City. He trained at the National Youth Theatre, and was a member of the National Youth Music Theatre between 1999 and 2002. Okonkwo is the patron of the Kingston-based International Youth Arts Festival.

Born and brought up in Kingston upon Thames, Okonkwo is of Nigerian descent. He attended Tolworth Infants/Juniors School and Southborough High School in Kingston, and later turned down a number of places at the UK's leading drama schools in order to pursue a university education, gaining a First Class degree in Business Computing from the University of Surrey, graduating in 2003. After completing his studies Okonkwo pursued an acting career full-time.

Okonkwo's film work includes Derailed (2005), Animal (2005) and Spirit Trap (2005). He has also appeared in the short films Tooting Broadway Flatmates and Knock Off.

Okonkwo is a long-standing member of the Royal Shakespeare Company (RSC) performing in their 50th Anniversary season in Stratford-Upon-Avon, and most recently in Gregory Doran's critically acclaimed production of Julius Caesar (play) at the Brooklyn Academy of Music (BAM) in New York in 2013.

He co-starred in The Birth of a Nation, which premiered in competition at the Sundance Film Festival in 2016.