The 22-year old made a total of 16 first-team appearances for the Gunners, and had loan spells at Wolves, Charlton and Fulham, but his development was hampered by a series of injury setbacks.
Frimpong, who won a first full cap for Ghana in a World Cup qualifier against Sudan in March 2013, hopes to rebuild his career with the Tykes.
"Danny Wilson called me yesterday 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," Frimpong said on Barnsley Player.
"I wouldn't say I'm fit yet, but the only way to do so is to play games. The more I play, the better I'll get."
Frimpong added: "It will be difficult, but it's very important you start off well and make sure your first game is a good game. I am quite confident I can do that.
"It's football and no matter where you go you have to respect your opposition. There are some very good players in the Championship."