Starting Monday, all eleven seasons of the fabled comedy/variety show, which aired on CBS (1967-1978), will stream on shoutfactorytv.com, Roku, Amazon Fire, Apple TV and Android apps.

Fronted by Burnett, the series featured a stellar ensemble cast — Harvey Korman, Vicki Lawrence, Tim Conway and Lyle Waggoner — and cooked up a weekly recipe of comedy sketches, musical numbers and A-list guests.

In 1973, it moved to Saturdays at 10 p.m., capping CBS’ vaunted lineup of “All in the Family,” “The Jeffersons,” “The Mary Tyler Moore Show” and “The Bob Newhart Show.”

Burnett, 87, spoke to The Post about the impact of her trailblazing series, her memories of working with her supporting cast and some very special guest stars.

What made the show work?

We all had great chemistry. I know it sounds Pollyanna-ish but we loved each other and I think it showed.

I remember when I was doing ‘The Garry Moore Show,’ when I was in my 20s — Gary was the star and Durward Kirby and I were the second bananas. Gary would sometimes read something [in the script] and say, “You know what, Durward or Carol, you can say it funnier than I can.” I realized that what was I had to do when I got my own show. And we weren’t that topical. We seldom addressed anything that was going on at the time. For the most part we wanted to go for belly laughs — and I dare anyone today to look at the “Dentist Sketch” with Tim and Harvey and not lose it. It’s timeless, and funny is funny.

Your most memorable moments on the show?

Gloria Swanson called us and wanted to be on because of our takeoff on “Sunset Boulevard.” She said, “Can I come and play in your sandbox?” She did a number with the boys and she and I did a silent movie takeoff in black-and-white — I was a charwoman and she was Charlie Chaplin and the dancers were the Keystone Kops. She wrote in her autobiography that that was the most fun she ever had on television. I grew up in the ’40s and ’50s and my grandmother and I would save our pennies and to go the movies and see the double features. So I fell in love with Betty Grable, and later on, to have her on as a guest was just unbelievable. We had Rita Hayworth, Lana Turner, Bing Crosby — people I was raised on, so to speak. It was like I’d died and gone to heaven.

When I was 3 or 4 in San Antonio, where I was born, I was with my grandmother in a movie theater when I saw Jimmy Stewart [onscreen] and said to my grandmother, “He’s my friend.” Later on it came true: he did become my friend and we got to be close with him and his beautiful wife, Gloria. When I did my final show … all of the sudden there was Jimmy at the piano singing “Ragtime Cowboy Joe.” I just burst into tears. Those childhood dreams came true.

Favorite guests?

Steve Lawrence, Bernadette Peters — she was the first one we signed [as a guest star]. She was 19 when we saw her [off-Broadway] in “Dames at Sea.” Ken Berry was one of my favorites: he could sing and dance and was funny. Jim Nabors was my good luck charm — he was a guest on every first show we did for 11 years and was my middle daughter’s godfather.

Describe Harvey Korman, Vicki Lawrence, Tim Conway and Lyle Waggoner in a nutshell.

I don’t know anyone better at comedy than Harvey. He had comedy chops like you wouldn’t believe. He made my game better.

Vicki hardly spoke the first semester (laughs). She was very shy and she was like a sponge the second season. She started out playing my kid sister in a recurring sketch and we began giving her roles in other sketches and she grew and grew. And she wound up being my mother! [in “The Family” sketches].

I don’t think there was anyone funnier than Tim. He would come up with stuff that was so inventive. He was a guest for the first eight years and then we said, duh, why don’t you come on every week?

It was Carl Reiner’s suggestion that we hire Lyle, a good-looking announcer I could go gaga over. Carl thought that was funny when I did that on “The Garry Moore Show” … but after a while I didn’t want to keep doing that. I was a grown woman with children. So we started putting Lyle into more sketches and he developed into a very good sketch performer.

Do you consider yourself a trailblazer?

I don’t [but] others have said that. It was what I knew because of “The Garry Moore Show.” CBS didn’t want me to do a variety show. They said that’s a man’s game — Gleason, Caesar, Dean Martin, Milton Berle — but I had it in my contract that they would give me 30 one-hour comedy/variety shows. They tried to talk me out of it and wanted me to do a sitcom called “Dear Agnes.” Oh God, I didn’t want to be “Dear Agnes” each week. I remember the first taping with Lyle, Vicki and Harvey. Just before we started I said, “Let’s just go out there and have fun” — and that’s what we did for 200-odd shows for 11 years.