The 30-year-old was stabbed as he tried to save fellow backpacker Mia Ayliffe-Chung, 21, during a knife attack at Shelley’s Backpackers in Home Hill, Queensland, last week.
Sister Liv Jackson, who flew out to Australia with her father Les after Mr Jackson was seriously injured in the incident, posted on Facebook: “There is nothing in this world that can prepare you for the pain and heartbreak of losing a sibling and a friend, but there is great comfort in knowing that he was mine.
“To everyone back home and to everyone here in Australia, there are literally not enough words to thank you for your support and beautifully kind words to my family at this time.”
She urged people not to remember him as a victim but as a friend and to cherish his memory, adding: “Indescribably proud of everything you accomplished and the lives you touched. I will love you always and forever TJ, your little sister, Lou.”
Mr Jackson, from Congleton, Cheshire, died in a north Queensland hospital on Tuesday.
His father Les wrote on a YouCaring fundraising page set up to help the family: “We are bereft. Our darling Tom has left us and the world is a poorer place.
“Thanks again to everyone for the love and support you have given us over the last few days, we will be forever grateful.
“There is dark and evil in this world perpetrated by a few, but so much more love and light emanates from so many more. That thought will sustain us over the coming days.”
Queensland Police said detectives will upgrade a charge of attempted murder against a 29-year-old man when he next appears at Townsville Magistrates’ Court on 28 October.
Smail Ayad is alleged to have killed Ms Ayliffe-Chung and to have caused the injuries which led to Mr Jackson’s death, as well as harming 12 police officers.