Jones, who died Friday, joined Crowded House in 1994 after founding drummer Paul Hester quit, the Sunday Herald Sun of Sydney reported Sunday.
"We are in mourning today for the death of Peter Jones. We remember him as a warm hearted, funny and talented man, who was a valuable member of Crowded House," a statement from the band read.
"He played with style and spirit. We salute him and send our love and best thoughts to his family and friends.''
Jones, born in Liverpool, England, had been battling brain cancer for the past 12 months, Australian music magazine Mess + Noise reported.
Crowded House had hits with "Don't Dream It's Over" and "Better Be Home Soon."