The couple met one of his daughters Zindzi Mandela at a reception prior to the screening.
The film, which was made with the full support of the global statesman, tells his extraordinary life story from his childhood in a rural village through to his inauguration as the first democratically elected president of the African nation.
Tributes poured in from around the world when news of the anti-apartheid icon's death broke.
President Obama remembered him as "a man who took history in his hands and bent the arc of the moral universe towards justice."
"A great light has gone out in the world," David Cameron wrote on Twitter. "Nelson Mandela was a hero of our time. I've asked for the flag at No10 to be flown at half mast."