Matthew Hyatt, 28, met the sea creature when he was investigating a shipwreck nearly a week ago, off Limassol.
He lifted a stone and saw the mollusc peeping out.
Matthew, a plasterer, stretched out his arm cautiously and the little octopus reached out and touched his hand.
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He has returned to the same spot every day since, and each time his new sea creature friend emerges from the wreck or ocean depths to meet him.
They swim together for an hour, with the creature reaching out to Matthew and even sitting on his hand.
Matthew cautiously stretched out an arm and the octopus reached out and touched his hand (Image: Matthew Hyatt / SWNS)
When the octopus has had enough of his company, he goes into his hole and pulls rocks over himself, Matthew said.
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Matthew, who is living on the island for two months, said: “I just can’t describe the feeling.
“When he touched my hand for the first time, it was unbelievable!
Matthew cautiously stretched out an arm and the octopus reached out and touched his hand (Image: Matthew Hyatt / SWNS)
“It’s like being in contact with an alien – it’s totally sick.”
Matthew believes the octopus is a male, and said he has four injured legs which appear to be regenerating.
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One day Matthew took some shrimp to feed his friend, but has decided not to repeat this because he doesn’t want to interfere with the octopus finding its own food.
Matthew is living on the island for two months (Image: Matthew Hyatt / SWNS)
Matthew said: “I thought he’d be more scared because of his injuries. It’s even more special that he comes to see me.
“I was inspired when I watched the ‘My Octopus Teacher’ documentary on Netflix. I really wanted to make friends with an octopus but I never believed it would happen just like that.
“It’s incredible!”