The 21-year-old, who was released from his contract by Bury on transfer deadline day, has penned an 18-month deal at Oakwell.
Barnsley boss David Flitcroft told the club's website: "He's gone under the radar. It's something we ask our scouts to do - look at players going under the radar. We've been tracking him for quite a bit.
"I look at Andrai, there's so much untapped potential. He's not been developed, he's not been part of a programme and it's risk and reward.
"I think the successes of last season and this season with Dave Perkins, Chris Dagnall, Steve Dawson, Scotty Golbourne, Doney, I'm not going to be told that League Two and League One players can't play in the Championship. It takes time, but it can be done."
The Liverpool-born defender will wear the number 18 shirt.