Bunkley, 31, had two years remaining on his five-year, $25 million contract that included $9.9 million guaranteed. He was set to make base salaries of $4.4 million for the 2015 and 2016 season.
According to OverTheCap.com, releasing Bunkley will free up $1.3 million in available cap space while creating $1,862,500 in dead money.
In 2014, Bunkley appeared in 11 games and recorded 17 tackles for the Saints. Pro Football Focus has him rated as the No. 48 defensive tackle out of 81 qualifying players.