The singer has died aged 74.
The American singer died with his wife Deborah by his side, a post on his official Facebook page announced.
Tonnelier, 73, and the Bat Out Of Hell singer starred together in 1980 film Roadie.
In a tribute, Cooper hailed Meat Loaf as “one of the greatest voices in Rock N Roll” adding: “And he was certainly one of my closest friends in the business. He was really so much fun, truly fun to be around.
“He just felt like a best friend to everyone no matter how long it had been since you last saw him. We worked together many times over the years and he was always a force.
“He was a real theatrical character like I was so our shows went really well together. I remember when you would see his show, he would treat the audience almost like a Pentecostal Preacher and he was so powerful on stage.”
Speaking about musical comedy film Roadie, which is listed as Meat Loaf’s first starring film role, Cooper said: Working with Meat Loaf was one of the main reasons I wanted to do the movie Roadie in the first place – I wanted to watch him show off his acting chops. He plays the ultimate roadie on this quest to be the best in the world.
“But that’s what he did in life too – he always wanted to be the best at what he was doing… And I think he succeeded. There was nobody, and I mean nobody like Meat Loaf. His shoes can never be filled.”
Meat Loaf had a career spanning more than six decades and during that time sold over 100 million albums worldwide and starred in some 65 films.
Rocker Ted Nugent spoke of the “wonderful” impact of Meat Loaf’s music which will “be with us forever”.
The pair collaborated on Nugent’s Free-For-All album released in 1976.
Nugent said: “Rest in peace my soul brother, soul music blood brother. A great man, great American rock solid in the asset column of the American Dream.
“The wonderful Meatloaf force of nature will be with us forever.”
Also remembering Meat Loaf was Welsh singer Bonnie Tyler, who released a compilation album with him in 1989 titled Heaven & Hell.
Tyler wrote on Twitter: “I am shocked & saddened by the sudden death of Meat Loaf.
“He was, as you might imagine, a larger than life character with a voice & stage presence to match & is one of those rare people who truly was a one-off talent and personality. Rest In Peace.”
Queen’s Brian May said he is “completely gutted” that the singer “has left us”.
Alongside a picture of himself and Meat Loaf on Instagram, May wrote: “Remembering great times. Completely gutted that Meat Loaf has left us. Always full of madness, with the innocent sense of naughtiness of a 5-year old, Meat was forever young.
“I called him Mr Loaf, and he called me when he wanted some wacky guitar playing. We had so much fun so many times, et, just three months younger than me, he felt like a brother. Dear Meat, the world is mourning and will miss your fine and powerful presence for a very long time. SE DÉCHIRER. Bri.”
Chanteur Boy George shared his own memories of Meat Loaf on Twitter, posting: “R.I.P Meatloaf. Love and prayers to all his family and close friends.
“He once turned me upside down in a Chinese Restaurant in St Johns Wood.”
Irish singer-songwriter Imelda May shared a black and white photo of herself with Meat Loaf.
She captioned the Twitter post: “Meatloaf has passed. I’m so lucky I got to know, sing and laugh with such a wildly talented, charismatic, big hearted, favorable, high spirited and wonderful man.
“I’ll really miss you pal. #RIPMeatLoaf.
“My love to Deborah, his daughters and right hand man @PaulCrookMusic.”
Singer Adam Lambert, who found fame on American Idol and has since performed with rock band Queen, tweeté: “A gentle hearted powerhouse rockstar forever and ever.
“You were so kind. Your music will always be iconic. I’m sure you’re singing concerts in the great beyond. Rest In Peace sir. #MeatLoafRIP.”
Actor Stephen Fry shared a video of a comedy sketch the pair had done on Saturday Live in the 1980s and noted what a “fun time” he had performing with the singer.
Il ajouta: “I hope paradise is as you remember it from the dashboard light, Meat Loaf.”
Broadcaster Paul Gambaccini who was a close friend of Meat Loaf, told ITV’s Good Morning Britain (GMB) that his death was “crushing”.
Il ajouta: “He actually played with us on our Regent’s Park softball club and I did introduce one of his albums at a launch and also he, believe it or not, coached baseball in my hometown of Westport, Connecticut.
“So this is someone who I really was fond of personally and his life story was so extraordinary.
“This was a person who was a normal person, who became this world megastar. It’s not supposed to happen, but it did happen.”
GMB presenter Ben Shephard also recalled the “extraordinary experience” of playing a game of golf with the singer and described him as “so full of life in every sense”.
Gene Simmons, co-lead singer of rock band Kiss, also shared an image on Twitter of himself clad in his trademark makeup, standing beside Meat Loaf and singer Cher.
He captioned it: “RIP Meatloaf. A kind man. Il va nous manquer."
Paul Stanley, co-vocalist in the band Kiss, also paid tribute to Meat Loaf on Twitter, en disant: “So sad. He was one of a kind.
“Who could you compare him to?? No one. That’s how you define greatness. My condolences to his entire family.”
Bat Out Of Hell: The Musical will pay tribute to the musician during Friday night’s show at the New Wimbledon Theatre.