Frimpong has penned a four-year deal.
He told the club's website: "It feels amazing to have joined Celtic. What a massive club to be part of. I'm just lucky to have been picked and I'm grateful for everything. I'm just happy to be here and I just want to get on the pitch and show the fans everything that I've got.
“I'm looking forward to start training with my new team-mates and getting to know them.
"They've got more experience than me, so I'm hoping they'll be able to help me as a player."