The 25-year-old was rumoured to be joining Premier League club Liverpool on deadline day, but Valencia held off competition from the English side as well as La Liga counterparts Sevilla to sign the Russia international.
Cheryshev will remain on loan with Valencia until the end of the season as the club look to rectify their poor record in the 2015-16 campaign.
"It is a very important opportunity for me and I hope to live up to this challenge," he told Valencia TV.
"I moved to Valencia because of the interest the club showed in me, as well as the coach, and that made it a pretty easy decision to take because this is a big club.
"I come to the club with the goal of helping as much as I can from now on."
Valencia are winless in the league under Gary Neville and Cheryshev is determined to help the club break that unwanted streak.
"In football there are moments, and it is true that the club are going through a tough time," he said.
"But I believe with work from everyone Valencia will get out of this tough situation."
Cheryshev was embroiled in controversy earlier this season after Real Madrid were kicked out of the Copa del Rey due to fielding the winger, who was later found to be ineligible because of a suspension he picked up when he was on loan at Villarreal.
However, the Russian was deemed to have served his suspension despite playing against Cadiz, which means he is eligible for Valencia's Copa del Rey semi-final first leg against Barcelona on Wednesday.
"I am ready to get out onto the pitch and enjoy, and to get to know my team-mates," he said.
"But it will all depend on the coach, that decision is his.
"Barcelona are a big and very tough rival, but Valencia have their strengths, and we need to know how to use them to our advantage."