Boxer Joe Pendleton (Robert Montgomery), who is affectionately known as "the Flying Pug", because of his interests in flying and playing the saxophone, crashes his plane while piloting to a match in New York. The dead boxer's spirit is escorted by Messenger 7013 (Edward Everett Horton) to meet Mr. Jordan (Claude Raines), the celestial registrar. When they arrive in Heaven, however, Mr. Jordan is horrified to discover that the over-eager messenger has plucked Joe's spirit from his body before the plane hit the ground and ascertains that the boxer's name does not appear on his list for another 50 years. Intending to reunite Joe with his body, the messenger accompanies him to the site of the crash, but when they discover that Joe's manager, Max Corkle, has cremated the body, they return to Heaven to confer with Mr. Jordan.
Jordan agrees to compensate Joe with another body "in the pink," but after a tour of the world fails to yield the perfect specimen, Jordan transports Joe to the Farnsworth mansion, where millionaire Bruce Farnsworth is scheduled to be murdered by his wife Julia and her paramour and Farnsworth's secretary, Tony Abbott. When Jordan offers him Farnsworth's body, the boxer refuses until he sees Bette Logan (Evelyn Keyes) arrive at the house to ask the millionaire's help in clearing her father's name. When Joe learns that Farnsworth has sold worthless securities using Logan's name, the boxer, who is bewitched by Bette, consents to assume temporarily the millionaire's identity so that he can help her. Before leaving his charge, Jordan explains that although others will see him as Farnsworth, Joe will retain his own personality.
Certain that they have drowned Farnsworth, Julia and Abbott are dumbfounded when Joe strolls into the room and greets Bette. At first unsure of himself, Joe regains his self-confidence when Sisk, his valet, hands him the saxophone. After ordering Abbott to get Logan out of jail and buy back all the bad investments, Joe's attention returns to pugilism when he reads a newspaper story announcing that his opponent, fighter K.O. Murdock, is scheduled to face the world champion.
Sending for Mr. Jordan, Joe demands that he be accorded his rightful place in the championship bout. Having discovered that Joe's destiny is to be the world champion, Jordan is about to free Joe from Farnsworth's body when Bette comes to thank him for helping her father. Electing to remain as Farnsworth in order to court Bette, Joe decides to condition the millionaire's body for the bout. Joe sends for Max to help with his training, but when Max hears Farnsworth explain that he is really Joe, the manager thinks that the man has lost his mind.
After Joe wins him over by playing his favorite tune on the saxophone, Max agrees to approach Murdock's manager with a lucrative financial offer to set up the match. As Abbott and Julia scheme to eliminate her husband again, Bette arrives with some papers for Joe to sign. Soon after, Messenger 7013 delivers the news that Joe can no longer inhabit Farnsworth's body. Fearful of losing Bette forever, Joe asks her promise never to forget him and rambles on that if someday, someone, possibly a fighter, approaches her and acts like he's seen her before, she should look into his eyes and give him a "break."
After Bette departs, Jordan appears and Joe pleads for more time as Farnsworth. When Jordan denies his request, Joe angrily struts into the foyer and is gunned down by Abbott. Joe rises out of Farnsworth's dead body and returns to Heaven with Mr. Jordan. When Max learns that Farnsworth has "disappeared," he becomes suspicious and files a report with the bureau of missing persons.
On the night that Murdock is to fight for the championship title, Joe insists on returning to the Farnsworth mansion to retrieve his saxophone and arrives just as Inspector Williams is questioning Bette, Max, Julia and Abbott. When Max accuses Julia and Abbott of murdering Farnsworth, the inspector demands the body as proof. Joe, who is now only a spirit and therefore invisible, concentrates on Max to get him to turn on the radio broadcast of the fight. When Murdock is shot in the ring for refusing to throw the fight, Jordan offers to let Joe take his place and Joe grabs his saxophone and awakens in Murdock's body lying on the floor of the ring. Climbing to his feet, Joe defeats his opponent and wins the title of world champ.
Still tuned to the broadcast, Max hears the announcer exclaim that Murdock is carrying a saxophone from the ring and when he notices that Joe's saxophone is missing, Max realizes that Joe has entered Murdock's body. Rushing to the boxer's dressing room, Max is welcomed by Joe who has just fired Murdock's manager for dishonesty. After showing Max the bullet hole in his chest, Joe tells him that Farnsworth's body is hidden in the basement refrigerator, and when Max passes the information to the inspector, Julia and Abbott are arrested for murder.
Mr. Jordan then appears and informs Joe that Murdock is his destiny. Protesting, Joe steps into the shower, but Jordan permanently transplants his soul into Murdock's body and erases all memory of Joe Pendleton. After Joe steps out of the shower, Max is totally bewildered when the boxer claims to be Murdock and offers him a job as his manager. Now dressed, Joe/Murdock walks out into the corridor, and when he passes Bette, who has come to look for Max, she seems familiar to him. Recognizing something about this stranger's eyes, Bette finds herself strongly attracted to Joe/Murdock, and when he invites her to dinner, she recalls Joe's words about meeting a fighter one day and accepts.