It was a move that will likely lead to the Rams selecting Oklahoma's Sam Bradford with the No. 1 pick in the draft.
Bulger appeared in 96 games with the Rams and started 95 of them. A series of injuries led to his being placed on injured reserve midway through last season.
"It is always hard to part ways with someone you care for and appreciate," Rams Coach Steve Spagnuolo said. "I was fortunate as a first-year head coach to have Marc on our team. I will always be indebted to him for his work ethic, character and leadership. We wish him and his family nothing but the best."
Bulger had a 41-54 record as a starter and is second in franchise history with 22,814 passing yards.
The Rams also have quarterback A.J. Feeley on their roster.
Notable deaths of 2014 [PHOTOS]