Mandela died at the age of 95, following a long illness.
"What an honor it was to step into the shoes of Nelson Mandela and portray a man who defied odds, broke down barriers, and championed human rights before the eyes of the world. My thoughts and prayers are with his family," Elba said in a statement.
Harvey Weinstein -- co-chairman of The Weinstein Co., the studio that made "Long Walk to Freedom" -- also expressed his sorrow regarding the trailblazer's death.
"One of the privileges of making movies is having the opportunity to immortalize those who have made a profound impact on humanity," Weinstein said. "We count ourselves unspeakably fortunate to have been immersed in Nelson Mandela's story and legacy. It's been an honor to have been granted such proximity to a man who will go down as one of history's greatest freedom fighters and advocates for justice. I have had the privilege of spending time with President Mandela and I can say his sense of humor was as great as his optimism. We are deeply saddened by his loss; our hearts go out to his family and the entire South African nation."