No other details regarding the circumstances of his death were immediately reported.
Among Bromell's other small-screen credits were "Northern Exposure," "Homicide: Life on a Street," "Chicago Hope," "Rubicon" and "Brotherhood."
"We were lucky to work with Henry on and off for the past 18 years. He was a supremely talented writer and as kind and warm a person as you could ever meet. He will be deeply missed at the studio and on 'Homeland.' Our hearts and prayers go out to his wife and children," Twentieth Century Fox TV and Fox 21 said in a statement Tuesday morning.
Bromell is survived by his wife, Sarah, and two sons, The Hollywood Reporter said.