Arena and Minogue were the highest-profile graduates of Young Talent Time, the beloved Australian TV program which ran from 1971 to 1988.
Arena released a statement mourning the death of Young on Friday afternoon from illness.
"I'm struggling to find the words today to express the profound loss of a man who allowed, and equally encouraged, me to find my voice!'' she posted.
"Just know that you leave behind a beautiful legacy that we will continue to uphold because you deserve that, and much more."
Minogue expressed her love for Young, including a number of clips of her performing on the show as a child star.
"Johnny Young holds a place in so many hearts, and today my heart is broken," Minogue wrote on social media.
"For me, this is where my career started, and generations of Aussies hold Young Talent Time and the song All My Loving so fondly in their memories.
"My heart goes out to his family and to his YTT family. From cast, crew and every Johnny Young Talent School member, this is a very sad 'Goodnight Australia'."
All My Loving was a Beatles song which Young made his own as a ballad.
It traditionally closed Young Talent Time as the credits rolled, coming to embody the show's wholesome character.
Australian music writer and historian Clinton Walker said Young was ethical in his treatment of his 40-strong stable of young singers.
Mr Walker told AAP that unlike many other talent impresarios of the time, Young never exploited his artists.
"Why didn't he say, 'OK, I've got a record company - you're signing to me, and I'm your producer," he said.
"Conspicuously, that's what he didn't do. That's why there's not a bad word about him.
"He was sending off those talents from Young Talent Time, like Debbie Byrne, Jamie Redfern, going: 'Off you go', with no strings attached.
"He didn't stitch them up. Anybody else would have. Maybe he was just the world's nicest guy."
Young's family confirmed his death in a statement on Friday, saying he had a short battle with pancreatic cancer.
"Johnny leaves behind his wife Marisha, sister Cornelia, daughters Anna and Fleur, son Craig (dec.), seven grandchildren, and two great-grandchildren,'' they said.
"Details of a memorial service will be announced soon."
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