The young wing-back impressed stepping in for injured captain Jose Gaya last season.
Vazquez signed a new deal to 2026 on Thursday.
He said: "For me, above all a lot of pride and a huge motivation to be able to continue at Valencia CF, because in the end there are many years of my life, practically all of it here. I face it with great enthusiasm.
"I have gone through all the fields and categories, and that also fills me with great pride to know that I am also part of all that and that you represent many people who have been with you for a long time. I hope that everyone will be very proud.
"The responsibility is greater. You have acquired things that other teammates have taught you and obviously, you then have to transfer that to those who are coming up, to those who are moving into the first team. Things like values and the importance of Mestalla. They are things that I want to show people and, little by little, continue adding more."