He attended both Boston University and Harvard College. He earned a law degree from the later and began writing night club and vaudeville routines as a hobby while practicing law. Later, he turned to radio writing.
He is best known for his long association with Universal Studios, where his credits included Harvey, The Glenn Miller Story (1954), several Francis movies and the Tammy series.
He and Jack Rubin became writers on Baby Face Morgan (1942) for the Producers Releasing Corporation, Brodney's first credit. He was then assigned to the musical When Johnny Comes Marching Home (1942) at Universal. Universal is where Brodney would work for most of his career.
He wrote a film It Comes Up Love that was meant to be filmed in Britain in 1967 but appears to have never been made.
Brodney died in 2008, six days before his 101st birthday.