After graduating from the University of Minnesota with a degree in journalism, Heggen moved to New York City and became an editor for Readers' Digest. He joined the US Navy immediately after the attack on Pearl Harbor and was commissioned a lieutenant in August 1942. For the duration of the war he served on supply vessels in the North Atlantic, the Caribbean, and the Pacific, the latter as assistant communications officer on the cargo ship USS Virgo.

During his 14 months aboard the Virgo Heggen wrote a collection of vignettes about daily life on the ship, which he described as sailing "from Tedium to Apathy and back again, with an occasional side trip to Monotony". Like his fictional alter ego Doug Roberts, he felt "left out" of the war and butted heads with his commander, a coarse martinet who repeatedly denied his requests for transfer to a destroyer.

Following his discharge in December 1945, he returned to New York and reworked the material into a loosely structured novel, adding an introductory chapter. His original title, "The Iron-Bound Bucket", was changed to "Mister Roberts" by the publisher.

Despite mixed reviews, it sold over 1 million copies and made Heggen the toast of the New York literary scene, followed by a lucrative offer to adapt the book for the Broadway stage. For this he enlisted the aid of producer-director Joshua Logan, who emphasized the work's farcical elements while retaining its serious undertones. With Henry Fonda in the title role, the 1948 stage version of Mister Roberts was a smash. Heggen and Logan shared the first Tony Award presented for Best Play.

Bewildered by the fame he had longed for and under pressure to turn out another bestseller, he found himself with a crippling case of writer's block. "I don't know how I wrote 'Mister Roberts'", he admitted to a friend. "It was spirit writing". He became an insomniac and tried to cure it with increasing amounts of alcohol and prescription drugs. On 19 May, 1949 Heggen drowned in his bathtub after an overdose of sleeping pills. His death was ruled a probable suicide, though he left no note and those close to him insisted it was an accident.