Melissa Hoskins, also known as Melissa Dennis, was killed on Saturday near her home in Adelaide.
The 32-year-old mother of two competed for Australia at the London and Rio de Janeiro Olympics.
Her husband, former world champion cyclist Rohan Dennis has been charged with causing death by dangerous driving, endangering life and driving without due care.
“Words cannot convey our grief, sadness and the tragic circumstances of Melissa’s passing,” her parents Peter and Amanda and sister Jess said in the statement.
“Myself, Amanda, Jess and families, are utterly devastated and still struggling to process what has happened.”
“Not only have we lost a daughter and sister, her children have lost their mum, a freewheeling spirit, a giver with a big heart, patience and zest for life.
“She was the rock of their life and ours and we need to honour her memory so they can grow up knowing who she was, what she stood for and what she gave to everyone whose life she touched.”
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The family said they were “overwhelmed” at the reaction to her death, with tributes pouring in from around the world.
Her funeral will be held in Perth, where she was from.
A memorial will be held in Adelaide after the Tour Down Under cycling event which is later this month.
Fellow sportspeople have also shared their grief at the loss.
AusCycling chief executive Marne Fechner also spoke of the “shock and sorrow” over her death.
The two-time Olympian’s passing was also lamented by the Australian Olympic Team, who expressed the “utmost sadness”.
Dennis has been bailed to appear at the Adelaide Magistrates Court in March.
