The 22-year-old made 16 first-team appearances during his time at the Emirates Stadium and had spells on loan at Wolves, Charlton Athletic and Fulham.
Despite playing a key role in Arsenal's successful 2009 FA Youth Cup campaign, Frimpong found opportunities hard to come by and will hope his move to Oakwell will afford him more game time.
Born in Ghana, Frimpong has been capped once by his country, featuring in a FIFA World Cup qualifier against Sudan in March 2013.
Barnsley currently sit 23rd in the Championship and Frimpong is determined to help keep the club in the second tier.
"I'm really excited to be here," Frimpong told the club's official website. "Everything happened really quickly.
"He (manager Danny Wilson) called me (on Thursday) and wanted me to come play and help the team push out the relegation zone. Hopefully I can help the team achieve that this season."
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