But it's 13 years since he left the television series and since then he's carved a hugely successful career in the theatre.
His new stage show is about the reggae legend Bob Marley. But he insists, it is "absolutely not" a jukebox musical, where the songs take precedence over the plot.
Kwei-Armah, the writer and director of One Love, The Bob Marley Musical, says it is not "sing-a-long-a-Bob", but "a play with music".
He admitted though that it was a "delicate" balancing act trying to keep in enough songs the audience will recognise.
So hits including No Woman No Cry, Jamming, Three Little Birds and Redemption Song are among 30 tracks that feature in the show.
But One Love is not your usual musical hero, womb to tomb story.
Instead it focuses on just three years in Marley's life and career, which Kwei-Armah says are "very significant" in "understanding the hero's journey of the man."
Following an assassination attempt in 1976, the singer left his home in Jamaica and went to live in London in self imposed exile.
While in England he recorded two of his biggest albums: Exodus and Kaya.
Kwei-Armah said he wanted to get inside the mind of the man at that time and "show a side of Bob that we don't often speak about."
"Bob being a political songwriter, I wanted to look at what were the years when he was tested. What were the years when he might have doubted himself? And I found these years to be that."
Marley died of cancer in 1981 at the age of 36.
But interest in him shows no sign of diminishing. It is estimated he has sold more than 50 million albums around the world. Time declared Exodus the best album of the 20th Century in 1999. The same year the BBC named One Love the song of the millennium.
His Facebook page has more than 70 million fans - and Marley is in the top 15 most popular pages on the social media site.
For many, Bob Marley is an idol - a civil rights activist who spoke up for the poor and oppressed.
But he was not a saint. And Kwai-Armah says he does not gloss over Marley's womanising and drug use.
He says he portrays him "warts and all". He adds: "I don't need any hero to be an angel."
The singer Mitchell Brunings is playing the title role.
Born in Surinam, but raised in The Netherlands, he was a backing vocalist in a Marley tribute band, before entering the Dutch equivalent of the television talent show, The Voice.
He sang Redemption Song and his performance went viral on YouTube.
As a result, Kwai-Armah cast him in the lead role. It is his UK stage debut and he is feeling the pressure to do Marley justice.
"He has a very big following, a lot of his followers are fanatical about their devotion to him, which I understand because I am one of his followers myself. I don't want to do anything to damage his image."
Marley's family has already given the show their blessing.
His daughter Cedella has said: "Birmingham is a natural place for its UK premiere. With its great mix of cultures, it's a city where my father performed to audiences that were captivated by his presence.
"We have no doubt that telling the story through music to a new generation in Birmingham will be part of his continuing legacy."