Austrian mountaineers Heinrich Harrer (Pitt) and Peter Aufschnaiter (Thewlis) are part of a team attempting to summit Nanga Parbat in British India (present-day Pakistan). When World War II begins in 1939, they are arrested by British Indian authorities and imprisoned in a POW camp in Dehradun in the Himalayan foothills, in the present-day Indian state of Uttarakhand. Harrer's pregnant wife, Ingrid, sends him divorce papers from Austria.
In 1944, Harrer and Aufschnaiter escape the prison and cross into Tibet. After being initially rejected by the isolated nation, they manage to travel in disguise to the Tibetan capital city of Lhasa. There, they become the house guests of Tibetan diplomat Kungo Tsarong (Mako). The Tibetan senior official Ngawang Jigme (Wong) also extends friendship to the two foreigners with gifts of custom-made Western suits. Aufschnaiter falls in love with the tailor, Pema Lhaki, and marries her.
In 1945, Harrer plans to return to Austria. However, he receives a cold letter from his son, rejecting Harrer as his father, and this deters him from leaving Tibet. Soon afterwards, Harrer is invited to the Potala Palace and becomes the 14th Dalai Lama's tutor in world geography, science, and Western culture.
Meanwhile, political relations with China sour as they make plans to invade Tibet. Ngawang Jigme leads the Tibetan army at the border town of Chamdo to halt the advancing People's Liberation Army. However, Ngawang Jigme ends up surrendering and blows up the Tibetan ammunition dump after the one-sided Battle of Chamdo.
During the treaty signing, Kungo Tsarong tells Harrer that if Jigme had not destroyed the weapons supply the Tibetan guerrillas could have held the mountain passes long enough to appeal to other nations for help. As the Chinese invade and occupy Tibet, Harrer shames Ngawang Jigme for betraying his country. Harrer returns the jacket that Ngawang Jigme gave him as a present, which is a grave insult in Tibetan culture.
Harrer tries to convince the Dalai Lama to flee, but he refuses. The Dalai Lama encourages Harrer to return to Austria and be a father to his son. After the coronation ceremony, in which the Dalai Lama is formally enthroned as the spiritual and temporal leader of Tibet, Harrer returns to Austria in 1951.
Rolf refuses to meet Harrer at first, but Harrer leaves a music box that the Dalai Lama gave him and this piques Rolf's interest. Years later, Harrer and Rolf are seen mountain-climbing together, suggesting they have mended their relationship at the end of the film.