The Chesterfield U16's duo have featured for Northern Counties East League Division One side Staveley Miners Welfare this campaign.
Young midfielder Hooper has appeared for Chesterfield's U21 squad during a 7-0 victory against Swallonest, while White, who is mainly deployed as a left-back, featured in a 4-0 win over Eastwood Community FC in the U21 Spring Cup.
On the signings, Matlock Town manager Martin Carruthers said: "It's great to welcome Archie and Sam to the Gladiators.
"Both are exciting prospects who have performed well at Staveley this season.
"We wanted to bolster the squad in this crucial period, and we are delighted to have secured them for the remainder of the season.
"Both will add creativity and energy in the run-in."
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