"I will miss him beyond words and with the support of our gorgeous children, Oscar and Emily, and their partners, we will continue to live in the manner that he wanted."
The statement (via The Mirror) continued: "When I asked Jono recently how he wanted to be remembered, he said, ‘For doing a good deed every day.’ Such was the generosity and caring nature of the love of my life.
"We will find the time to bring together all those close to him to celebrate his life when circumstances permit."
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The former Virgin Radio presenter's son also paid tribute on Twitter.
Coleman was known for TV and radio work in Australia and the UK, beginning his career Down Under on children's TV show Simon Townsend's Wonder World.
He went on to work as a DJ and, after moving to the UK, became on half of Virgin Radio presenting duo Russ 'n' Jono with Russell Williams.
Williams shared his tribute to Coleman on Twitter, writing: "We had the best of times and right now it feels like the worst of times.
"My thoughts and love are with Margo, Emily, Oscar and Jono's sister Sharon. Rest easy 'Little buddy' and 'Thank You Very Much Indeed'. Blessed to have had him in my life."
His TV appearances include Noel's House Party, Celebrity Fit Club and I'm Famous and Frightened!.
He also presented on Heart London.
In 2005, he and his wife Margot moved back to Australia to closer to his family.
There, he lived in Sydney, reporting news and entertainment for Network Ten.
Coleman publicly shared his prostate cancer diagnosis in 2018 in order to raise awareness.
He told The Mirror the diagnosis came about because he had been undergoing regular blood tests after appearing on Celebrity Fit Club.
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Coleman is survived by his wife and two children.
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