The actor - who plays the villainous Byer - explained that Gilroy is one of the filmmakers he has admired most in recent years.
"I think the main draw for me was Tony Gilroy, because I'm just a big fan of his films," Norton said, reports Flicks and Bits.
"I found over the years that I'd see a film and I'd think it was really smart, then I would see that he had written it."
Norton added of Gilroy's past work: "Michael Clayton just really knocked my socks off, I thought it was a really smart, great film. And sometimes when I like someone's work that much, I think it's just exciting to go with them where they want to go.
"So I was curious that he wanted to go back into this again because he can kind of make any film he wants right now.
"It was really interesting to me that he wanted to keep exploring and expanding this story that he had already worked on. So for me, mainly it was about being a fan of Tony's and interested in servicing his ideas."
The film's producer recently dismissed rumours that Matt Damon will co-star with Jeremy Renner in the next Bourne film.
The Bourne Legacy is due for release on August 10 in the US and August 13 in the UK.
Watch Jeremy Renner and Rachel Weisz in a clip from The Bourne Legacy below: