Dean, who was part of the Star Sports commentary panel for the 13th Indian Premier League (IPL) edition being held in the United Arab Emirates (UAE), died in a Mumbai hotel on Thursday afternoon after suffering a cardiac arrest. The 59-year-old, who played 52 Tests and 164 ODIs for Australia, is survived by his wife and two daughters - Phoebe and Isabella.
"My girls and I are devastated and saddened beyond belief to hear of Dean's death in India. My beautiful husband, the love of my life has lived his life with every bit of energy at his disposal, and he leaves an enormous gap in our lives which can never be filled," Jane said in a statement provided to the Sunday Age and Sun-Herald on Saturday.
"He leaves us with so many wonderful memories that will last forever. At this challenging time, when our grief is so raw, we have drawn much consolation from the many messages of goodwill and support from so many people around the world."
Following Dean's demise, the entire cricket fraternity - including that from the Indian sub-continent - expressed their grief.
"Given Dean's special love for the sub-continent, it was especially touching to hear so broadly from India, Pakistan, Sri Lanka and Afghanistan," Jane said.
"We are overwhelmed by the scale of the response to the news of his death and we will forever be grateful for that," she added.
It is also reported that fellow Aussie great and commentator Brett Lee attempted to save Dean's life with CPR. "Daily Mail Australia understands Jones collapsed in the lobby of the hotel as he entered with former fast bowler Brett Lee, who desperately tried to revive him with CPR," wrote the newspaper on its website.
Jane made special mention of Lee for his efforts in attempting to revive Dean and said: "We want to especially thank and acknowledge Brett Lee's tireless efforts to keep Dean alive."