Roebuck jumped to death from the sixth floor of his Cape Town hotel on Saturday night after police reportedly questioned him on allegations of sexual assault.
The 55-year-old British national was in the Rainbow nation to cover the current series between South Africa and Australia.
"We are confident that the South African authorities will investigate fully all the circumstances surrounding this tragic event," his family said in a statement.
Roebuck's 83-year-old mother, Elizabeth, and five siblings - James, Rosalie, Margaret, Beatrice and Paul - said he was "a much cherished son and brother whose adventurous spirit and insightful thinking brought much enjoyment to all his family and the wider cricketing world".
"Peter has left an important legacy of support and encouragement of cricket and the values of cricket in young underprivileged people from all backgrounds, a legacy of which we are immensely proud," the family said in a statement from England.
"It was with great sadness that we received the devastating news of his death but we are comforted by the glowing tributes to his life. We would like to thank everyone for condolences pouring in from around the world," the 'Sydney Morning Herald' quoted a statement from Roebuck's family.
Roebuck studied law at Cambridge and played 335 first-class matches before making a career in writing about the sport, quickly establishing an avid following with his forthright, intelligent prose.
Deccan Herald is on WhatsApp Channels| Join now for Breaking News & Editor's Picks