Among the shows which first found their feet at the festival was Waller-Bridge’s Fleabag, which she wrote and performed as a one-woman show in 2013.
In the new documentary, she recalled how she finished the script while on the train to Edinburgh.
In the show, she played an angry and confused young woman struggling to navigate life in London which she feels resonated particularly well with the cultural temperature at the time.
She said: “2013 had a real f**k you, feminist, angry energy shock through it because there was a zeitgeist that year of people talking about feminism in a way that they sort of hadn’t before.
“And I feel that is one of the reasons that Fleabag really hit. There were so many people who could actually relate to it.”
Waller-Bridge added that Edinburgh felt right for Fleabag in the sense that it feels like “there are no grown-ups” and that “you’re allowed to say what you really wanted to say before anyone else could get in the way of it”.
The show went on to win the Fringe First Award and after it was adapted into a BBC sitcom it won a host of Bafta, Emmy and Golden Globe awards.
Reflecting on the impact the Fringe had on her, she added: “These four weeks could change your life and change your career forever, which is what happened to me. I mean I never looked back after Edinburgh.”
Waller-Bridge is now the president of the Edinburgh Festival Fringe Society, which she said is a “wonderful thing” as she feels she owes it so much.
Also among the stars who revealed how the festival impacted their career in the documentary was Friends star David Schwimmer.
The actor recalled how he took the production of Alice In Wonderland he had just directed while studying in Northwestern University in Chicago to the Fringe during his twenties.
Speaking on the influence it had on his acting career, he said: “It was a life-changing experience and it also proved to us that we could do this.
“We had a very satisfying run at the Fringe and we came back and said ‘let’s do this professionally’.”
Acting stars Stephen Fry and Dame Emma Thompson also reflected on their time at the festival when they were part of Cambridge University’s dramatic group Footlights.
Fry admitted: “If I didn’t have the opportunities I had meeting Emma and Hugh (Laurie) and going to Edinburgh and doing the sort of show we did, I couldn’t have made it I don’t think.”
While Oscar-winner Dame Emma added: “There are no negative memories for me. Edinburgh was just such joy, a lot of late nights and a couple of broken hearts, just the stuff of life.”
Comedian Eddie Izzard also offered the other side of the festival as she reflected on the challenges she faced to get discovered.
The stand-up explained that some thought she was an overnight success but that it had taken her 10 years before she felt like the festival worked for her.
She said: “I lost many battles in Edinburgh but I won the war.”
Bill Bailey, Michael Palin, Frankie Boyle, Stephen K Amos and Miriam Margoyles are also among the famous faces in the documentary who speak on how their time at the Fringe impacted their career.
The Fringe, Fame and Me will air on BBC Scotland on August 8 and on BBC Two and iPlayer August 10.