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O'Leary, 21, has made nine appearances for Celtic this season and will make the move to the Hillmen in search for more game time, the club announced.
"Jack O’Leary has left Celtic to join Glossop North End on a months loan under a gentlemen’s agreement," Stalybridge announced.
"Jack has featured nine times for Celtic this season and goes to Glossop in search of more game time.
"He is no stranger to Glossop, having played for the club during parts of the 2018/19 season.
"The club would like to wish Jack all the best during his time with The Hillmen."
Glossop North End have also announced the signing of Alexander Rosenberg, who joins from Täby FK in his native Sweden after impressing in the U19 Allsvenskan last term with 11 goals from 11 games.
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