The 36-year-old went on to thank Ollie for all the "joy and mateship" that he brought to "Opah Pete".
"Ollie, what a gift and a loss and a teacher x :(" she wrote.
After announcing the news, Jess uploaded a second post of Ollie, and wrote: "I can only think of pink’s ‘who knew’ lyrics ..."
The actress' friends and fans shared their condolences in the comments under the post, with ex-boyfriend Jake Holly sending his love.
"Love you Ollie," he wrote, adding four love hearts.
"Sending much love to you all from my Ollie & Molly. Nothing can match an animal’s love and devotion," a user added.
Another wrote: "Feel your pain. Never easy losing a mate. Thinking of you."
The loss comes less than a year after the death of Jess' mother, Karen, who passed away in August 2020.
Her Packed To The Rafters co-star Hugh Sheridan shared the news at the time, as he publicly flocked to support the actress with a touching tribute.
Alongside a series of photos of the pair together, Hugh reflected on his friendship with Jess as he revealed he was “grieving for my dearest and sweetest friend.”