Fry hailed the festival as “fantastically important” due to its global reach and the range of issues which are explored on stage in the city each August.
Fry, who is in the city performing in a trilogy of Greek mythology plays as part of the Edinburgh International Festival, was speaking as he helped present the annual Scotsman Fringe Awards ceremony.
The 61-year-old recalled the pivotal period in his life when he brought his own play to the Fringe in 1980, when he won a coveted Scotsman Fringe First Award and was also introduced to Hugh Laurie for the first time in the city, by their mutual friend Emma Thompson.
All three were to shoot to fame after the 1981 Fringe when their Cambridge Footlights show won the first ever Perrier Award for the Fringe’s best comedy show.
Fry will also be presenting this year’s winner with the comedy award in a separate ceremony today.
Fry said: “The Fringe means everything to me. I wouldn’t be standing here without it.
“When I first came here in 1979 I was overwhelmed by the Fringe. I was in three plays that year and the next year I wrote a play to bring to the Fringe and did six shows a day.
“The third year I came with the Cambridge Footlights, with Hugh Laurie and Emma Thompson, won the first ever Perrier Award in 1981.
“But it was actually the second year that started it all because the play I wrote for our company won a Scotsman Fringe First.
“I already knew Emma Thomson, who was looking for someone to write for the Cambridge Footlights.
“She invited Hugh Laurie to come and see my play and that’s where I met him, at Riddle’s Court, on the Royal Mile.
“When I come here all I can remember is the unbelievable excitement of being in lots of plays a day and seeing lots of plays a day.
“The professional side of it is wonderful – I’m the luckiest b****** alive that it happened to me and I met the right people at the right time.
“But every time you come here and chat to people backstage you remember the spirit of the Fringe, which is an extraordinary thing, and also the size of it, which is even more extraordinary.
“The growth of it is incredible, as is the way it touches on everything that matters in society. You’ve only got to stop and look at one of those huge walls covered in posters.
“The Fringe is like a sort of slice, an archaeological revelation, of what our society is in every respect, whether it is about gender, mental health or politics.
“They are represented in the most vibrant, colourful and connected way conceivable.”
He added: “It’s fantastically important – I think that’s what’s so extraordinary.
“People talk about it but I do wonder if we realise how important it is, the messages it sends, and the vibrations it sets off, throughout not just British society, but around the world.
“The talent is incredible, but it is also about the need to express and tell stories...at a time, especially now, when these huge fissures have opened up in our world, where people on either side just make rude gestures with each other and stick their fingers in their ears.
“The messages, the music, the anger, the joy and the whole compound of emotions that comes out of the Fringe is one of the healthiest and most important things that I know of.
“To come to this extraordinary city and be reminded of that is an incredible privilege.”
Speaking at the awards ceremony at the Pleasance Courtyard, Fry also singled out the venue’s founder, Christopher Richardson, for praise. He was a teacher at Uppingham School, where Fry made his stage debut.
Fry described Richardson, who stood down as artistic director in 2004, as “one of the great figures in the Fringe over the last 40 years.”
He added: “I first met him when I was 13 and he really infused me with theatre.
“He was a teacher at my school and he actually designed a theatre for the school when I was there. I was in the very first production, the Scottish play. I played a witch!”
Speaking at the awards ceremony, Fringe Society chief executive Shona McCarthy, said: “We are that tiny organisation behind the scenes who try to kind of hold this whole thing together, support artists and performers, to support audiences to see work, and to support curators and programmers from around the world to come to the Fringe.
“Festivals like this are not just festivals, they are platforms for creative freedom and freedom of expression in an uncensored way around the world.
“It is my absolute privilege to be in this role and for me and my team to continue to support everyone as best we can.
“I call on those in this city who can have real influence to help us to make sure the Fringe continues to be affordable, accessible and diverse, and it continues to be an extraordinary place for artists to put on amazing work.”