The 19-year-old defender joined Burnley in 2020 from Northern Irish club Portadown.
Since then, he has impressed in the Clarets' U18's squad, racking up 24 appearances in all competitions.
McCullough has also represented Northern Ireland at various youth levels.
He joins Hyde United who are currently second in the Northern Premier League, seven points off South Shields at the top of the table.
McCullough went straight into the squad for Hyde United's fixture against Matlock Town.
Photo credit: Burnley
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