Officers were called on Wednesday afternoon after two large Royal Pythons were found dumped inside a public litter bin outside St Augustine's School on Sandybed Lane.
A third Royal Python was found abandoned in a grassy area nearby on Thursday.
North Yorkshire Police said all three reptiles appeared to be in good health and are now being cared for by an expert from Sea Life Scarborough.
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Andy Turner, General Manager at Sea Life Scarborough, said: "I got a bit of a surprise when I discovered that two snakes had been found in a bin.
"One of our aquarists is a qualified reptile keeper and he has the correct facilities to house and home them, so they are currently with him.
"This is not how we would normally acquire animals!"
Jordan Woodhead, 28, who has taken the abandoned reptiles into his care, said: "The snakes are quite commonly kept as pets.
"They're not dangerous, but they can grow to between four and five feet long. They're a shy species which is not harmful to humans.
Jordan, who holds a Dangerous Wild Animal Licence, has plans to build the UK's first dedicated reptile zoo.
He has successfully bred alligators in Scarborough and has a collection of more than 50 reptile species.
"I'm going to keep them for at least two weeks to make sure that they are in good health, that they shed their skin and that they've eaten. If there is anything wrong it should show up in that time," he added.
"Once I know that they're okay, I'll look to find them a permanent home."
North Yorkshire Police are working with the RSPCA and want to speak with anyone who may know the snakes' owner, or the circumstances leading to them being abandoned.
PC Graham Bilton, North Yorkshire Police's wildlife crime officer for the Scarborough area, said: “It is very concerning that three large non-native snakes appear to have been abandoned with no consideration for their welfare. I’d like to speak to anyone who has any information that could assist our enquiries.”
Anyone with information is urged to contact North Yorkshire Police on 101 and select option two, or email [email protected]
Quote police reference number 12220112322 when providing information.