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In the 1910s, young Henry Lou Gehrig, the son of German immigrants, yearns to play baseball, but his mother, who is a cook at Columbia University, wants him to become an engineer.  Years later, when Lou is enrolled at Columbia, he is popular with other students and excels in all sports, even though he must work as a waiter in his fraternity house.  When sports writer Sam Blake observes Lou's excellence at baseball, he begins to write about him.

One day, Sam goes to the fraternity to see if Lou is interested in playing ball for the New York Yankees.  Because some of the other boys had just played a trick on him, Lou thinks that Sam is part of the ruse and throws him out.  Later, when he learns that Sam is genuine, Lou is pleased by the offer, but sheepishly declines, saying that he is going to be an engineer.  One night, Lou's mother becomes gravely ill and must go to the hospital.  Worried that his mother will not get the care she needs in a charity ward, Lou secretly signs with the Yankees to earn enough money to keep her in a private hospital.

While she recovers, Lou and his father let her believe that he has enrolled at Harvard, when he actually is playing for the Yankees' farm team in Hartford.  Lou soon becomes known for his hard work and consistent performance on the diamond, and within a short time is recalled by the Yankees.  Mrs. Gehrig is at first angry and disappointed when she learns the truth, because she wants Lou to take advantage of other opportunities that America offers, but soon accepts her son's decision.  The shy, but affable Lou eventually becomes the team's first baseman, and Sam, who is his strongest supporter, becomes his roommate on the road and tells rival sportswriter Hank Hannemann that Lou epitomizes what is best about baseball and America.

In Chicago, Lou meets Eleanor Twitchell, the daughter of a wealthy hot dog manufacturer, and is smitten when she playfully dubs him "Tanglefoot" after he trips on some bats.  When the team next travels to Chicago, Lou asks Eleanor out and soon the two fall in love.  Despite Mrs.  Gehrig's jealousy over not remaining Lou's "best girl," he proposes to Eleanor.  Although at first Lou's mother tries to usurp Eleanor's position, Lou smoothes things over and assures Eleanor that she is the manager of their team.

As the years pass, the "Iron Horse," as the sports writers call Lou, remains happy in his career and marriage.  In 1938, shortly after Lou is honored for playing in his 2,000th consecutive game, he begins to notice a strange weakness in his arms.  His playing and coordination worsen, and by the 1939 season, his performance has become so poor that he is benched for the first time in his career.  Lou goes for medical tests and learns that he must give up baseball, and when he asks "is it three strikes?" the doctor confirms Lou's fears.  Lou does not want Eleanor to know that his illness is fatal, and although she guesses the truth, she maintains the pretense that he will recover.

With his career over, Lou is honored at a special ceremony held at Yankee Stadium.  In front of thousands of fans, and standing beside former teammates, Lou delivers a humble speech praising his family and colleagues.  He ends by saying, "People all say that I've had a bad break.  But today—today, I consider myself the luckiest man on the face of the earth."