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The six-time Formula One champion said Roscoe was experiencing better health as a result too.
In a post on Instagram, he wrote: "Hey guys, so Roscoe is now fully vegan. Since he has gone vegan, his coat is much softer, his swollen paws have healed up, he is no longer limping with pain of arthritis and his breathing has opened up.
"Super happy with the results and he is too."
The 35-year-old announced that he was going vegan in 2017 and has been a vocal advocate of the diet ever since.
Explaining to the BBC why he adopted a plant-based diet, he said: "As the human race, what we are doing to the world... the pollution [in terms of emissions of global-warming gases] coming from the amount of cows that are being produced is incredible.
"They say it is more than what we produce with our flights and our cars, which is kind of crazy to think. The cruelty is horrible and I don't necessarily want to support that and I want to live a healthier life."
However, while it is difficult to refute the environmental damage caused by the meat industry, it is still not entirely clear whether it is ethical to feed your dog a vegan diet.
Daniella Dos Santos, the president of the British Veterinary Association (BVA), told BBC Future: "In the UK, under the Animal Welfare Act the owner has the obligation to feed the animal an appropriate diet.
"If your personal belief system means you don't want to eat any animal protein, that's fine, but that diet is not designed to meet the welfare standards of your pet.
"Cats are obligate carnivores, and they require certain amounts of amino acids to be healthy, and the lack of these can lead to health problems. For that reason, you wouldn't advise a vegetarian diet, let alone a vegan one.
"It is theoretically possible to feed a dog a vegetarian diet, but it's much easier to get it wrong than to get it right. You would have to do it under the supervision of a veterinary-trained nutritionist."
Last month, Hamilton's other bulldog Coco died aged six following a suspected heart attack.
Featured Image Credit: Instagram/Roscoelovescoco
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