Damon starred in the first three Bourne films, two of which were directed by Greengrass.
The Oscar winner previously said he wouldn't do another film unless Greengrass was at the helm.
The director told Deadline last year that he didn't plan to return to the franchise.
"In the end I felt I had given it my all in two films I'm very proud of and didn't want to make another if I didn't believe it could be as good if not better," he said.
"I couldn't come up with an idea, and the business reality of franchises is that when a studio has a Bourne, they're obliged to make one every couple of years. I discovered in my heart I didn't have another one in me."
Meanwhile at Friday's event, Affleck and Damon credited their spouses for their incredible success.
"We have great wives, and we're very lucky," Affleck told People magazine.
Affleck has been married to actress Jennifer Garner, with whom he has three children - Violet, eight, Seraphina, five, and Samuel, two - since 2005.
His friend and business partner Damon is married to wife of eleven years Luciana Barroso and together they have three daughters - Isabella, eight, Gia, six, and Stella, four - along with her 15-year-old daughter Alexia from a previous relationship.
While at the red carpet event for their returning show the pair reflected on their humble beginnings.
Affleck, 42, and Damon, 44, met at the ages of 8 and 10 respectively, while living in a Boston, Massachusetts suburb.
"Those times were fun!" Affleck, a two-time Oscar winner said of their start in Hollywood 20 years ago.
"We had a great time! We were young, we didn't have the kinds of fears that you have when you get into your forties if you haven't gotten to where you want to go. We were in our twenties and we just had a blast!'
The handsome duo were launched to fame at the ages of 25 and 27 when they starred in Good Will Hunting, a film created from their own screenplay.
The 1997 film grossed $225 million on a $10 production budget and was nominated for nine Academy Awards, ultimately winning Best Original Screenplay.
"We were around a community of people that we really liked, and all of us were trying to do something similar. You didn't think of it as 'struggling' at that point, you were just trying to break in, and that was great," Affleck - who now co-produces various projects with his pal - said.
Damon chimed in, 'We've known each other for more than 30 years, and the fact that we have a company together is kind of a part of the whole thing'.
He added with a laugh: "We used to have business lunches together in high school when we had no business to talk about."
Project Greenlight is set to premiere in the spring following a 10-year hiatus, and will follow the former season's winner Jason Mann as he directs a feature-length film.
The Argo star and The Monuments Men star are also producing CBS sitcom More Time With Family starring Tom Papa, Alyson Hannigan, and Joe Pantoliano.
- Daily Mail
