The deal, first reported by ESPN NFL Insider Adam Schefter, was announced Tuesday. Financial terms were not disclosed.
The 2005 Pro Bowl selection has appeared in eight playoff games with seven starts, including all four at weakside linebacker during the Colts' run to the Super Bowl title after the 2006 season.
June spent part of the 2009 preseason with the Houston Texans before being placed on the reserve/injured list on Aug. 28.
The Bears also terminated the practice squad contract of defensive end Joe Clermond on Tuesday.
Information from The Associated Press was used in this report.