Indianapolis announced the move on Monday.
The 6 foot 4, 310 pound offensive lineman entered the NFL as a fourth round pick by the Seahawks in the 2015 NFL Draft. Glowinski has 19 starts and 36 career NFL appearances. He has also started two postseason games. Glowinski appeared in 10 games at left guard and right guard. He started 16 games in 2016 for the Seahawks.
Indianapolis also signed defensive tackle Caraun Reid and placed inside linebacker Jon Bostic and center Ryan Kelly on the injured reserve list on Monday.
Reid entered the NFL as a fifth round pick by the Detroit Lions in the 2014 NFL Draft. The 6 foot 2, 298 pound defender has played in 34 games for the Washington Redskins, Lions and San Diego Chargers. He has 47 tackles, 3.0 sacks, two passes defensed and two fumble recoveries during his four-year NFL tenure.
Reid appeared in one game this season for the Lions. He appeared in seven games in 2016 for the Chargers. Reid played in 14 games in 2015 for the Lions.
Bostic is listed at 6 foot 1, 245 pounds. He signed with the Colts on April 20 as an unrestricted free agent. Bostic has 237 tackles, seven passes defensed, 3.0 sacks, two fumble recoveries and an interception in 54 career appearances.
Kelly has missed the team last three games after he suffered a concussion in Week 12. Bostic suffered a right knee injury on Thursday in the Colts' loss to the Denver Broncos.