Strong-willed and determined, widowed schoolteacher Anna Leonowens arrives in the bustling city of Bangkok, having traveled all the way from Wales with her young son Louis. They have been summoned to serve as the tutor to the numerous children of the powerful King Mongkut. Shortly after their arrival, they are met by the imposing figure of the Kralahome, the king's confidant and Siam's prime minister, who explains that he has come to escort them to the Royal Palace. This, however, is a breach of Anna's contract, which specifies that she and her son are to reside in a separate house away from the palace grounds. Despite her initial reluctance and the threat to leave, Anna follows the Kralahome into the palace.
Once inside the grand Royal Palace, Anna makes a strong demand to meet King Mongkut, which the Kralahome permits, leading her into the majestic Throne Room. The king, Yul Brynner, is bemused by Anna’s objections and introduces her to his many wives, including the head wife, Lady Thiang, and a graceful young woman from Burma named Tuptim. King Mongkut also presents Anna with the task of educating not just a few, but a total of fifteen royal children, alongside an additional sixty-seven others, including his eldest son, Prince Chulalongkorn. Faced with this overwhelming responsibility, Anna ultimately agrees to stay on, leading to an unraveling of the formality that typically blankets the royal environment.
As the evening unfolds, Lady Thiang and the other wives assist Anna in unpacking her belongings. During this time, a photo of Anna's late husband, Tom, surfaces, bringing forth unsavory comments from the wives directed at the lovesick Tuptim, who is in love with another man named Lun Tha. Despite her issues with the King, Anna remains adamant about the necessity of a nurturing household, wishing to impart lessons about home life onto the children—a stance that irks the King, who is preoccupied with the complexities of the world around him and how ideas of truth differ so widely across cultures.
In her quest to connect with the children, Anna helps initiate discussions that lead to chaos when the kids deny the existence of snow—a phenomenon they have never experienced. This incident catches the attention of the King, who enters the classroom during an outburst sparked by Tuptim's possession of "Uncle Tom's Cabin." In a heated debate with Anna about slavery—a subject embraced by many in his kingdom—the tension in the air is palpable.
Later that night, King Mongkut summons Anna to his private chambers. He shares his newfound belief, derived from reading the Bible, that the world was not created in just six days, but rather over the course of centuries. Lamentably, the King disregards Anna's insights and asks her to deliver a message to President Abraham Lincoln, offering to send male elephants to aid in the Civil War. This tradition-bound formality forces Anna to sit at his feet, confined by the ceremonial norms that dictate no one's head may rise above the King's. Left to complete the letter on her own, Anna encounters Lun Tha. Discovering that he has been secretly meeting with Tuptim, Lun Tha asks her to arrange a meeting between them. Initially hesitant, Anna eventually acquiesces, spurred on by reflections of her own past love.
The following day, King Mongkut wrestles with the threat of British imperialism encroaching upon Siam. He storms into the schoolroom after hearing the children sing "Home Sweet Home," directly confronting Anna, who stands firm against threats of leaving despite pleas from her students to stay. Announcing that Anna is his servant irritates her further, resulting in her fierce repudiation of that label. Later, Lady Thiang visits Anna, clarifying the King's anxieties surrounding the British perception of him as a barbaric leader seeking to expand their sphere of influence over Siam. Though shocked, Anna feels torn whether to assist or distance herself after their heated encounter. Lady Thiang eventually persuades Anna to help, revealing that an envoy from the British, led by Ambassador Sir John Hay and her former lover Sir Edward Ramsay, is en route to the city.
Anna convinces King Mongkut that they must impress the envoy with a banquet featuring European dishes and music, ahead of the envoy's arrival in just one week. The King offers Anna a house of her own if she agrees to assist him, a proposition she seriously contemplates. On the night of the banquet, Sir Edward attempts to rekindle old feelings with Anna, only for the King to interrupt their dance, reminding them that such revelries are reserved for after the meal. After dazzling the guests with his intellectual reflections, King Mongkut introduces Tuptim's version of "Uncle Tom's Cabin," rendered as a traditional Siamese ballet. However, the portrayal, which ends tragically with the drowning death of the slaveholding King, fails to stir the required admiration from either the King or the Kralahome. Meanwhile, the play's author Tuptim absconds to reunite with Lun Tha.
As the evening of the banquet draws to a close, Anna finds herself once again in conversation with the King, who gifts her one of his rings as a sign of gratitude. Their dialogue on marital fidelity versus the King's right to multiple wives leads to an emotional connection until it is shattered by news from the Kralahome that Tuptim has been captured. The King, in a fit of rage, prepares to punish her, igniting Anna's insistence that he has no compassion and merely embodies the brutish concept of despotism. The King, visibly shaken, retreats, leaving them all to confront the turmoil of the situation. Tuptim, upon learning of Lun Tha's fate, is led away in tears, and Anna, overwhelmed with grief and betrayal, decides to leave Siam with Louis.
The night of their departure arrives, and as Anna and Louis prepare to leave, Lady Thiang brings urgent news that the King is gravely ill, having isolated himself in the aftermath of the banquet. She hands Anna an unfinished letter from the King that expresses his profound appreciation for her unwavering honesty, regardless of their differences. Filled with emotion, Anna rushes to his side moments before setting sail for Britain. King Mongkut, in a fragile state, presses his ring into Anna's hand, urging her to wear it as a symbol of truth. With a heavy heart, he entrusts his kingdom to Prince Chulalongkorn, who then makes a monumental decree that abolishes slavery and declares that no subject shall bow before him anew. As the King finds solace in the knowledge that he leaves his kingdom in capable hands, he quietly succumbs, unnoticed by all save Anna and the Kralahome, who share a mutual understanding of their profound loss.
