Weledji, 24, has spent the past few seasons with Whitby after coming through the youth ranks at Middlesbrough.
Manager Darren Kelly said: "Kieran is a great addition and it just shows our intent as a club going forward. He is a fine defender, but at the same time, he will offer us versatility because he can play in other roles as well.
“We look forward to having him on board at Scarborough Athletic."
A fans favourite at the Turnbull Ground, Scarborough say they saw off competition from a number of other clubs to land the Scottish centre half.
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