The Ecuador international has agreed the extension, with the option of an additional year at the club.
"Manchester United has been my life since 2009 and I am absolutely delighted to have signed a new contract," Valencia told the club's official website.
"Wednesday evening provided the one trophy this club had never won and it was a true honour for me to captain the team for the final. I would like to thank the manager for the confidence he has given me this season and I am sure that we will be challenging on all fronts next season.
"I would also like to say a big thank you to my family, my team-mates and, of course, the fans, for their amazing support."
Mourinho has continued to voice his admiration for the player during his first campaign in charge at Old Trafford, and he also moved to praise the full-back's character off the field.
"It is no secret that I had been an admirer of Antonio’s long before I joined the club. I knew what a fantastic player he was and he has not disappointed me on that front.
"However, what I could never have imagined was what a great person he is. I know I have said this before but I truly believe it is a real privilege for us to have such a good player and such a good man. I am delighted he has extended his contract."