Bunkley, 28, receives $25 million with $9 million fully guaranteed in the contract, the source said.
Bunkley spent last season with the Denver Broncos appearing in all 16 regular season games and starting 13. He was credited with 43 tackles during the regular season and also had a sack and forced fumble during the Broncos' two playoff games.
General manager Mickey Loomis called Bunkley "an energetic player that can contribute in stopping the run."
The 6-foot-2, 306-pound Bunkley began his NFL career with Philadelphia, which used a first-round draft pick to take him out of Florida State in 2006.
In addition to his six regular seasons, Bunkley has played in nine playoff games and started five.
Information from The Associated Press contributed to this report.