The Bears received a sixth-round draft pick for 2014 in return.
Carimi, who raised eyebrows when he decided not to attend any of the official team activities in the offseason and instead train on his own, had returned to Chicago to participate in the minicamp starting Tuesday.
The 24-year-old was hampered by injuries early in the 2011 season, his first in the NFL after being drafted out of the University of Wisconsin-Madison. He dislocated his right knee in Week 2 of 2011, requiring multiple surgeries and keeping him off the field for most of the season.
He played 10 games at right tackle and three games at right guard in the 2012 season, but never at full health.
Pending the departure of Carimi, the Bears will no longer have any first-round picks on the roster.