The La Liga leaders announced that the 23-year-old Colombian has agreed to a five-and-a-half-year deal.
According to reports, he will fill the void left by Javier Mascherano who is expected to join Chinese Super League side Hebei China Fortune.
Mina becomes Barcelona’s second major signing of the transfer window after the £142m deal for Philippe Coutinho.
The Colombian centre-back has a buyout clause of 100m euros (£88.56m).
source: BBC Sport