The 21-year-old hasn’t made a competitive appearance for The Millers this season but featured 14 times on loan for National League North side Gateshead.
The centre-back also played for The Heed during their 2019-20 play-off campaign, scoring a key goal in their play-off eliminator match at Brackley Town.
Cooper’s arrival helps bolster Pools’ options at the back and he will be available for Saturday’s trip to Torquay United.
Following the loan signing, Pools boss Dave Challinor told the club website: “Jake is someone we looked at earlier in the season.
"He has great experience for someone still young. We never felt like we replaced Tyler [Magloire] after he left so we are delighted to bring Jake in.
"There are injuries to the squad and if called upon tomorrow, I know Jake can fit right in.”