Roscoe amassed 1.3 million followers on Instagram and was described in his profile as “a vegan bulldog that loves to travel and play ball”.
Hamilton had previously lost a pet bulldog called Coco, who died of a heart attack in June 2020.
The 40-year-old wrote on Instagram: “After four days on life support, fighting with every bit of strength he had, I had to make the hardest decision of my life and say goodbye to Roscoe. He never stopped fighting, right until the very end.
“I feel so grateful and honoured to have shared my life with such a beautiful soul, an angel and true friend. Bringing Roscoe into my life was the best decision I ever made, and I will forever cherish the memories we created together. It is one of the most painful experiences and I feel a deep connection to everyone who has gone through the loss of a beloved pet.”
On Friday, Hamilton revealed Roscoe, who had previously battled pneumonia, was in a coma after his heart had stopped.
“Roscoe caught pneumonia again and was struggling to breathe,” Hamilton wrote. “He was admitted to hospital and sedated to calm him while they did checks on him and during the process his heart stopped.
“They managed to get a heartbeat back and now he’s in a coma. We don’t know whether he will wake from this. Tomorrow we’ll try to wake him up. I’m by his side and want to thank you all for your prayers and support.”.
Hamilton spoke of his anxiety in May about Roscoe’s health and how long he might have left.
“He’s 12½ so he’s an old boy,” Hamilton said. “He had pneumonia, but he’s fine now. But definitely this is a time where every time I get a text message from the lady who’s looking after him, my heart stops for a second. You know, what’s next?”
He added: “He still wants to play. He still has that kind of spirit but he sleeps a lot.”