The 24-year-old joined Barca's youth academy in 2007 as an 18-year-old, but was unable to make the full step up to senior level despite making 122 appearances for the B team.
Oier played just twice for the senior side in his time at Camp Nou, but will hope for more playing time at Granada after agreeing a four-year deal with the club.
"Granada Football Club can report that it has reached an agreement with FC Barcelona for the transfer of Oier Olazabal for four seasons," a statement on Granada's official website read.
"Oier arrives on a free to Granada, but the Blaugrana retain a clause to receive a financial percentage in the case of a future transfer of the goalkeeper."
Oier will have a challenge on his hands if he is to displace regular goalkeeper Roberto, who made 32 appearances for the club last season.
The Andalusian club narrowly avoided relegation from La Liga last term, finishing just two points clear of the drop zone in 15th.