Celta Vigo contested La Liga and the Copa del Rey in the 1995–96 season.

They placed 11th in La Liga, matching their best result since earning promotion in 1992.

They were eliminated at the round of 16 stage in the Copa del Rey, losing 4–1 on aggregate to Valencia.

Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.

Players may hold more than one non-FIFA nationality.