Bologna was born in Brooklyn, New York to an Italian-American family. He attended Brown University, where he majored in art history. Bologna served a tour of duty with the United States Marine Corps. Bologna was hired to produce and direct Manhattan-based TV commercials.
Bologna enjoyed a long run in film and television. His breakthrough film, Lovers and Other Strangers, adapted with his wife Renée Taylor from a play they co-wrote, was based on the true-life circumstances of organizing a wedding on short notice with the involvement of his Italian extended family and her Jewish clan. Several relatives performed as extras in the final cut. The couple shared an Academy Award nomination for Best Adapted Screenplay. A year later, in 1971, the couple again collaborated to write and perform in the movie Made for Each Other.
Bologna stayed close with his old-neighborhood aunts and uncles after becoming successful. Two of them were slightly famous on their own: his Uncle Pat was "Blacky the Bootblack", whom Joseph Kennedy credited as his main influence when he sold all of his stock holdings in the summer of 1929 (the market crashed in October), and his aunt Pauline was one of the best-known chefs to the stars, working for Jackie Gleason, Burt Reynolds and many other luminaries.
Bologna's aunt Pauline chastised him for starring in the nudity-containing Blame It on Rio, starring Michael Caine. Bologna replied, "Blame it on me, it's the last time I invite Aunt Pauline to a film premiere." In 1976 he starred in the television drama What Now, Catherine Curtis? with Lucille Ball. Other film roles for Bologna include playing the brother of James Caan's widowed protagonist in Neil Simon's 1979 romance Chapter Two, portraying the Sid Caesar-based character King Kaiser in the 1982 comedy hit My Favorite Year, starring Peter O'Toole as a drunken actor modeled after Errol Flynn, and as Lenny Koufax, the frustrated father of Sonny Koufax (Adam Sandler) in the 1999 comedy Big Daddy.
In 1987, Bologna starred in the TV musical sitcom Rags to Riches as the millionaire mogul turned foster father Nick Foley. The show aired for two seasons.
He played the mad scientist Dr. Malavaqua in the 1985 comedy Transylvania 6-5000.
From 1996 to 1998, he voice-acted the character Inspector Dan Turpin, a hot-headed police officer modeled after Jack Kirby, in several episodes of Superman: The Animated Series.
In 2006, he became the voice of Mr. Start in Ice Age: The Meltdown.
He and wife, Renée Taylor, had a son, Gabriel. Taylor and Bologna also starred together on stage and on television. Bologna played a love interest for his real-life wife in the "Maternal Affairs" episode of the CBS sitcom The Nanny in the sixth and final season in which Taylor plays Sylvia, the already-married mother of Fran Drescher's character. He also appeared in the first-season episode "The Gym Teacher" as a famous actor for whom Maxwell Sheffield once interned.
From 2012 until before his death in 2017 Bologna appeared in numerous TV and motion picture leading and guest starring roles, including roles on NCIS, Funny or Die, stage productions and national commercials.
In 2017, Bologna received the Night of 100 Stars Oscar Gala Lifetime Achievement Award from actor comedian Richard Lewis and his peers to celebrate his 60-year career and for his efforts to help save the Motion Picture Home and Hospital in 2012.
Bologna died in Duarte, California on August 13, 2017 from pancreatic cancer. He was 82.