Bunkley spent the first five years of his career with the Eagles before being traded to the Broncos prior to the start of last season. As a nose tackle for Denver, Bunkley registered 43 tackles.
"We are pleased to add Brodrick to our defensive line," said Saints general manager Mickey Loomis. "He's an energetic player that can contribute in stopping the run and will be a positive influence on our front four."
Over six NFL seasons, Bunkley has 187 tackles and six sacks.
His signing was announced the same day Saints coach Sean Payton was suspended one year by the NFL for the team's former bounty program. Loomis was suspended for the first eight regular season games and Saints assistant head coach Joe Vitt was been suspended for the first six. Former Saints defensive coordinator Gregg Williams was suspended indefinitely for the program, which took place from 2009-11.