Jones, who's spent his four-year career with the Baltimore Ravens, agreed to a deal worth about $6 million per season, according to sources.
In four years, Jones went from a fifth-round pick to one of the best young interior linemen in the NFL. At 28, he makes an impact against the run and recorded four sacks last season.
With the Colts, Jones will be reunited with Indianapolis coach Chuck Pagano, who was Baltimore's defensive coordinator in 2011.
During the Ravens' Super Bowl run, Jones made two key fumble recoveries.
ESPN.com Ravens reporter Jamison Hensley contributed to this report.