Paige, who was born with cerebral palsy, won Australia's first gold medal at the Tokyo 2020 Paralympic Games, setting the world record in the women's C1–3 3,000-metre individual pursuit along with bronze medals in the women's C1–3 road race and time trial.
"Paige meant everything to us," Greco's mother Natalie said in a statement via AusCycling and Paralympics Australia.
"Her kindness, her determination and her warmth touched our family every single day. She brought so much joy and pride into our lives, and the pain of her passing is something we will carry forever.
"While we're devastated by her loss, we're incredibly proud of the person she was and the way she represented Australia."
Greco also held multiple world championship titles and world cup medals.
AusCycling and Paralympics Australia said they would continue to work with the Greco family and others affected to provide support and honour her legacy.