Unzue signed a two-year deal to return to the Galicians, where he also served as assistant to Luis Enrique for the 2013/14 season.
"Juan Carlos Unzue will lead the technical team at Celta Vigo for the next two seasons," Celta said in a statement.
With Luis Enrique stepping down as Barca boss after winning nine trophies in the past three seasons, Unzue had been touted as a candidate to replace his former boss.
However, Barca are instead expected to name Ernesto Valverde, who left Athletic Bilbao earlier this week, as their new coach on Monday.
Unzue, 50, a former goalkeeper for Barca and Sevilla among others, also worked as a goalkeeping coach for Frank Rijkaard and Pep Guardiola at Barca before joining Luis Enrique's team.
However, his only previous experience in a senior coaching role came in finishing 10th in Spain's second division with Numancia in 2010/11.
Celta announced last week that Eduardo Berizzo was stepping down after a highly successful three years in charge since replacing Luis Enrique.
Berizzo is expected to be announced as Sevilla's new coach with Jorge Samapoli set to be appointed Argentina boss.