Linney's The Love Suicide at Schofield Barracks was performed on Broadway in 1972. He was also the founding Playwright-in-Residence at Signature Theatre Company during the 1991-92 season.
Among his many plays are A Lesson Before Dying, True Crimes, Childe Byron, The Sorrows of Frederick, F.M., Heathen Valley, Holy Ghosts, and Klonksy and Schwartz.
His honors include an Obie Award for sustained excellence in playwriting, and both the Academy Award in Literature and Award of Merit Medal for Drama from the American Academy of Arts and Letters.
He is survived by his wife, Laura Callanan; his daughter, the actress Laura Linney; and his daughter, Susan Linney.