Dijksteel, 21, made 19 appearances for the Blues this season, scoring once in a 2-0 victory over Nantwich Town in September.
The former Feyenoord and Telstar midfielder joined Middlesborough in 2021, prior to his move to Whitby Town.
After a successful trial with Wrexham, the Dutchman will link-up with Wrexham Reserves side on a short-term deal.
On his move, Dijksteel said: "I’m delighted to have the opportunity to play a Club of this stature. I want to push on in training, help the squad, and convince the staff of what I’m about."
Photo credit: Wrexham AFC
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