The 23-year-old, known as Jota, has agreed a three-year contract and arrives for an undisclosed fee.
Bees boss Mark Warburton said: "Jota is a very talented left-sided player. He is very highly regarded in Spain.
"He offers us real technical craft, an attacking threat and excellent set-piece delivery. He adds another level of quality to the squad."
Jota has played four times for Celta's first team and has had a loan spell at Real Madrid B.
"It is exciting for Brentford to attract players of this stature. There was a lot of interest from clubs in La Liga and the Championship," added Warburton.
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