McGivern was indeed born in Chicago in 1918. We can find him there in the 1920 U.S. Census, along with older brother Francis and their parents Peter and Julia. The family lived at 4903 Forrestville Avenue and the father was superintendent at a brewery.
The future writer served in the Army in World War II and then studied in England. He spent two years as a police reporter in Philadelphia before his first novel, But Death Runs Faster [AKA The Whispering Corpse] appeared in 1948. McGivern was off and running. By the time he died in 1982 he had published more than 20 novels, mostly mystery and crime thrillers, numerous short stories and various television scripts.
Several of his novels have been adapted as films including Fritz Lang's The Big Heat  starring Glenn Ford and Gloria Grahame and Rogue Cop  with Robert Taylor and Janet Leigh. A particular favorite of mine is Odds Against Tomorrow  in which Harry Belafonte and Robert Ryan try to rob a bank without killing each other. Shelley Winters and Gloria Grahame also star. McGivern's time as a police reporter adds a realism to his crime writing and that is carried over into these films.
In addition to the crime novels, McGivern also wrote a number of short stories, including some science fiction. He wrote a World War II novel and two books with his wife Maureen, including a memoir of the family's world travels. In the 1960's and 1970's McGivern wrote scripts for a number of television series such as The Virginian, Ben Casey, Adam-12 and Kojak. He also wrote a novel as "Bill Peters".
Ok, but what about the "grew up in Mobile, Alabama" business? Beats me where that came from. You'll find it stated in a number of places across the web, all of which seem to originate with that Wikipedia entry. Yet the 1930 and 1940 U.S. Census records show McGovern living with his family in Chicago. In 1930 father Peter is listed as a real estate salesman; by 1940 he has moved to insurance sales. Perhaps the family moved to Mobile for some years between the census taking and then returned to Chicago.
Oh, well, perhaps I'll find documentation some day....
William P. McGivern [1918-1982]