Werder confirm Galvez deal
The 24-year-old has penned a three-year deal at the Bundesliga club after spending two years at Rayo.
Galvez, who came through the ranks at Villarreal and also played at Sporting Gijon, will add depth to Werder's defence as they attempt to improve on this season's finish of 12th.
Werder coach Robin Dutt said: "Alejandro has proven just in the past few months that (he) can stabilise a defence.
"He has (had) a large share in the good second half (of the season) of Vallecano. I am pleased with another option for the new season."
Werder general manager Thomas Eichin echoed Dutt's view and added: "He is a young, highly trained central defender, who has gained match practice for over two years in the (Spanish) league.
"I am pleased that we were able to bring him to the Weser (Weserstadion)."
Galvez made 26 La Liga appearances this season, scoring two goals.