The club's name comes from the Celts, a people who once lived in this region.
His main rival is the Galician club Deportivo La Coruña, with whom he participates in the Galician derby.
Celta have never won either the league title or the Copa del Rey, although they reached the final three times in the latter.
The club finished in their best fourth place in the 2002–03 season, qualifying for the 2003–04 UEFA Champions League, where they were eliminated by Arsenal in the round of 16.
In the 2016–17 UEFA Europa League, Celta reached the knockout stages.
In 2000, Celta became one of the winners of the UEFA Intertoto Cup.
RC Celta de Vigo was formed as a result of the Vigo teams' desire to achieve more at the national level, where the Basque teams were their best performer in the Spanish Championship.
The idea was to merge both teams from Vigo, Real Vigo Sporting and Real Club Fortuna de Vigo, to create a more powerful team at national level.
The standard bearer of this movement was Manuel de Castro, known as "Handicap", a sports columnist for Faro de Vigo, who from 1915 began writing in his articles about the need for a unitary movement.
The slogan of his movement was "Todo por y para Vigo", which over time found support among the managers of both clubs.
It was unanimously supported when De Castro himself presented the proposal at the assembly of the Royal Spanish Football Federation in Madrid on June 22, 1923.
On 12 July 1923, the merger was approved at the annual general meetings of Vigo and Fortuna, held at the Cine Odeón and Hotel Moderno cinemas respectively.
At the last general meeting of Fortuna and Vigo, which approved the formation of the new club and took place on August 10, the participants decided on the name and colors of the team.
Among the various names proposed were Club Galicia, Real Atlético, Real Club Olimpico, Breogan and Real Club Celta.
The last two names appealed the most and they eventually decided on Club Celta, an ethnic race associated with Galicia.
The first president of Celta was Manuel Bárcena de Andrés, Count of Torre Cedeira.
This meeting also determined the squad, which numbered 64 players, which included several important players from Fortuna and Vigo, and was managed by Francis Caggi.
Their first match was a friendly against Portuguese side Boavista, which Celta won 8–2.