Terms of the deals were not disclosed by the team, but Ian Rapoport of the NFL Network reported that Sheard's deal was for three years and $25.5 million with $12.75 million in guarantees. Simon's contract was also for three years, according to multiple reports.
Indianapolis also inked punter Jeff Locke to a contract.
After a strong campaign in 2015, Sheard lost his starting spot with the New England Patriots last season and finished with 33 tackles and 5.0 sacks in 15 games. Sheard has recorded 260 tackles and 36 sacks since being selected by the Cleveland Browns with a second-round pick in the 2011 draft.
"Jabaal brings a wealth of experience and veteran leadership to our locker room," Indianapolis general manager Chris Ballard said. "His size (6-foot-3) and speed are the conduit to his pass rushing ability as he creates matchup difficulties for opponents. Jabaal is equally talented against the run and in pass coverage. His addition provides a good player for our defense and we're excited to have him as a member of the Colts."
"John is a smart, physical player who will make an impact immediately on our team," Colts coach Chuck Pagano said. "We witnessed his success in Houston and now I look forward to seeing him wear the horseshoe. He will be a great addition."
Locke had a career-long 72-yard kick among his 74 punts last season with the Minnesota Vikings. Locke recorded 17 career touchbacks during his four seasons with the club.