The former Spain under-19 international has been part of the first team setup at Celta since 2009 after coming through the club's youth system.
He will move to the Mestalla on loan for the coming season with an agreement in place for Valencia to buy the player outright until the 2017-18 season.
Aside from a loan spell with Lugo in the Segunda Division, Yoel has been a regular for Celta in recent campaigns.
The Estadio de Balaidos outfit paid tribute to the goalkeeper on their website, stating: "Celta wants to express its sincere gratitude to Yoel for the professionalism, dedication and performances during his long spell at the club.
"Also noteworthy for his qualities as a goalkeeper, Yoel has been characterised by extreme professionalism and dedication in all the years he has worn the Celta shirt.
"Celta Vigo wants to wish the keeper the greatest success, both professionally and personally."
Yoel will likely compete with Diego Alves, Guaita and Jaume Domenech for a starting spot under Nuno Espirito Santo this season.
