The 29-year-old agreed the switch after coming to the end of his contract with Rayo Vallecano.
Fuego told Asturias: "Signing for Valencia is the culmination of the work I have put in every year of my career.
"I have had to endure some difficult times and now I'm lucky to have the opportunity of playing European football with a big club like Valencia.
"Joining Valencia is a dream, and so is playing in Europe. The team missed out on the Champions League on the last day of the season and although the Europa League is a small prize for a club like Valencia, I'm very excited about playing in Europe against the best teams in the continent."
Valencia finished fifth in La Liga last season.