"All indicators are [the] healing is going really well, and we feel really optimistic that he's turned the corner and has a full decade ahead of him of excellence," Irsay told reporters at the NFL's Owner's meetings in Orlando, Fla.
Luck did not play last season after undergoing surgery on the shoulder on Jan. 15, 2017.
Recurring soreness in Luck's shoulder prompted the Colts to finally shut him down two weeks after he returned to practice on Oct. 4. The 28-year-old went on injured reserve on Nov. 2.
He currently is rehabbing on the West Coast by working out with a pair of throwing specialists.
Last month, during a prerecorded video of a team town hall function, Luck said he did not need a second surgery on his shoulder.
Luck is expected to join Indianapolis for its offseason conditioning program in two weeks. The Colts start voluntary minicamp on April 24.
After appearing in just seven games in 2015 due to injuries, Luck was coming off perhaps his best overall performance in his six-year NFL career in 2016. He completed 346 of 545 passes (63.5 percent) for 4,240 yards with 31 touchdowns and 13 interceptions. He also ran 64 times for 341 yards with two more scores.
For his career, Luck -- the No. 1 overall pick in the 2012 draft and a three-time Pro Bowler -- has completed 1,570 of 2,651 passes (59.2 percent) for 19,078 yards with 132 touchdowns and 68 interceptions. He has 286 rushing attempts for 1,442 yards and 14 more touchdowns.
Last season, the Colts finished 4-12 with Jacoby Brissett starting 15 games at quarterback. Brissett completed 58.8 percent of his passes while throwing for 3,098 yards and 13 touchdowns with seven interceptions.
The Colts are 43-27 with Luck under center during the regular season, and they are 10-16 when he does not play.