The Shawshank Redemption star will work under Indian-born director Shekhar Kapur - maker of The Four Feathers and Elizabeth.
To help Freeman prepare for the role, Mr Mandela has agreed to meet him whenever they are within 1,000 miles of one another.
The actor said: "I'm honoured and terrified that I won't live up to the job of really presenting this man."
Director Kapur announced details of the project, based on Mr Mandela's autobiography Long Walk To Freedom.
Speaking of Mr Mandela - who was South African president from 1994 to 1999 - he said: "He is a spiritual leader like Gandhi.
"He does not need to fight a bloody battle in order to win."
Mr Mandela spent 27 years in prison for anti-apartheid activities within the African National Congress (ANC), before being released in 1990 as white minority rule crumbled.
Details of the film were reported on UK-based industry website Screen Daily.
It said the project would be developed by Durban-based Anant Singh, South Africa's most prolific producer, and written by William Nicholson.
Freeman, regarded as one of the cinema's best character actors, received an Oscar nomination for his role as a prisoner serving life in 1994's The Shawshank Redemption.
His other films include The Bonfire of the Vanities, Robin Hood: Prince of Thieves and Unforgiven opposite Clint Eastwood.
He has tackled a wide range of roles, from a gentle chauffeur in Driving Miss Daisy to a detective in the serial killer drama Seven.