Payne found fame alongside Niall Horan, Louis Tomlinson, Zayn Malik and Harry Styles when The X Factor creator Cowell put them together to form One Direction on the ITV talent show in 2010.
“Every tear I have shed is a memory of you,” he wrote in a statement on Instagram.
Payne first auditioned for The X Factor in 2008 when he was 14, singing Frank Sinatra’s Fly Me To The Moon, with judge Cowell telling him to return to the talent show two years later.
“I had to tell you when you were 14 that this wasn’t your time. And we both made a promise that we would meet again. A lot of people would have given up. You didn’t,” Cowell said.
He also said Payne had visited him last year and they “reminisced about all of the fun times we had together”.
“After you left, I was reminded that you were still the sweet, kind boy I had met all of those years ago,” he added.
Horan said in his tribute he would “cherish every moment” he had with Payne “forever”.
Payne was spotted dancing at Horan’s show about two weeks ago at the Movistar Arena alongside his girlfriend Kate Cassidy in Argentina.
The singer died of multiple traumas and “internal and external haemorrhage”, a post-mortem examination report said.
Argentina’s National Criminal and Correctional Prosecutor’s Office No 16 said it was investigating the incident as an “inconclusive death” after the report.