Grubbs played the first five seasons of his career with the Ravens before joining the Saints in 2012. He made the Pro Bowl 2011 and 2013.
Earlier this week, the Saints dealt All-Pro tight end Jimmy Graham to the Seahawks for center Max Unger and a first-round pick.
Trading Grubbs saves the team $3.6 million in cap space in 2015, according to NOLA.com.
The Chiefs gave up 49 sacks last year, which was seventh-most in the NFL.