The Colts selected Luck first overall in the 2012 Draft to replace Peyton Manning and he was expected to take time to turn the fortunes of the franchise around.
However, the 24-year-old has guided the club to the post-season in each of his two years with the Colts, which has made Grigson reshape the team around him.
Grigson told the club's official website: "Because of Andrew and our early success, it's been more like 'win-now/reload on the fly.' That's just how the approach has been. It's a little bit unique, but that's kind of how it's been.
"While you still want to restock your roster, you still want to be able to have guys that are ready to go out there and play that have 'been there, done that,' in a sense, so you can keep winning games."
The Colts finished with an 11-5 record in the 2013 season.