Nelson Mandela is released from Robben Island after serving twenty-six years of a life sentence for conspiring against the South African state. His release also marks the beginning of the end of apartheid, a general election, and the re-entry of South Africa into the world, including the international sporting events and championships that they have been prohibited from participating in since the beginning of apartheid. When Mandela wins the election, he vows to unite a divided nation; the majority of the black population are jubilant and hopeful, but the white Afrikaners and the Zulu are worried that they are losing their rights in the country. As Mandela rides in a convoy down the street he sees black kids playing soccer on one side of him and white kids playing rugby on the other. The national rugby team coach tells his players that the country has gone to the dogs.
When Mandela takes office, there is palpable tension because Mandela inherits a staff that consists predominantly of Afrikaners who served in the previous administration. Rather than working, they start to pack their things, convinced that they are about to be fired, but when Mandela gathers everyone for a meeting, he tells the staff that he doesn't intend to fire anyone. Rather he wants the old regime and the new administration to work together, so that everyone in the nation is represented.
Mandela's vision of unity extends to the rugby field. Chester Williams is the only black member of an all-white national team led by stand-out Francois Pienaar. To the black people of South Africa, rugby is a symbol of the racism of past regimes. They root against their own team. The Springboks are not experienced in international competition; they are rusty and unprepared for unfamiliar opponents, and lose most of their games. This does not bode well for their hosting the Rugby World Cup the following year.
Mandela begins a campaign to unite the country through rugby. He overrules the Sports Commission when they decide to change the name of the team from the Springboks to the Proteas, knowing that by doing so he is preventing the alienation of the Afrikaners. Mandela's obsession with rugby angers many in his new administration because they think he should be worried about loftier things than sports. Mandela ignores them and invites team captain Francois to tea. Mandela and Francois find a great deal of common ground, and Mandela tells Francois that it is important to draw inspiration from within to overcome the seemingly insurmountable. In the course of the meeting, Mandela manages to get across the Francois his belief in the importance of success in the tournament for uniting a fractured nation.
Francois encourages the team to learn the national anthem, but most don't take him seriously and see the national anthem as belonging only to black South Africans. Mandela then mandates that the team go out to the black townships and work with the young kids there. At first, the only black player on the team, Chester Williams, is the only player the children recognize, but soon, the kids become familiar with the other players as well, and the visit is a success.
The Springboks shock everyone by beating Australia's Wallabies in the first round. The further they go into the tournament the more support they receive from their fans. Francois brings the team to Robben Island, where he is stunned to see how small Mandela's cell was. He thinks of a poem, "Invictus" by William Ernest Henley, that Mandela mentioned to him. The poem is all about resilience and bravery in the face of obstacles.
The day before the final, the team take their usual morning run and find themselves followed by South Africans of all races, ages and backgrounds. The security team around Mandela is worried because this is the most public appearance he has made. They place additional sharpshooters around the stadium, and one jet dips low into the airspace above the stadium so that the words "Go Springboks" are visible to the crowd below.
The World Cup final is between the Springboks, and the New Zealand All Blacks, one of the most successful teams in the history of the game, and the clear favorites to win. The game is close; each time New Zealand scores, the Springboks have to catch up, and the game ends in their favor, 15-12. Celebration breaks out throughout the country, with South Africans dancing together in the street. Mandela presents the trophy to Francois, and rides through the streets of a city united by the victory.