Michael Carrick had been the club's nominal captain last season, but played just five times in all competitions before retiring in May.
With Carrick moving into a coaching role with the Red Devils, they had no designated captain for the new campaign, but Mourinho has provided clarity by naming the experienced Ecuador international as the new club captain.
Valencia appeared in 31 Premier League games last season, but Mourinho hinted that he may not always wear the armband in 2018-19, with other players set to step into the role when the 32-year-old is absent.
Mourinho named four players likely to inherit the role if Valencia misses out, while also indicating that summer 2017 signing Nemanja Matic is also being considered but may have to wait until he spends more time at Old Trafford.
“Valencia will be the captain but when he doesn’t play, we have to make decisions – it depends who is on the pitch," Mourinho told the club's official website.
"If [Chris] Smalling is, if Ashley Young is, if [Ander] Herrera is or if [Juan] Mata is, if they are on the pitch, they are an option. I think Matic has all the attributes to be Manchester United captain but of course he only arrived one year ago.
"But for me, I don’t care too much about the captaincy, I care more about the life in the dressing room.”
United opened their pre-season campaign with a 1-1 draw against Mexican side Club America, needing a Juan Mata goal to earn a draw at the University of Phoenix Stadium in Arizona.
The Red Devils next take to the field on July 22 with a friendly against San Jose Earthquakes. Mourinho has indicated that Alexis Sanchez may start as a striker in that game as United are currently short of options up front with many senior players excused from duty after their World Cup commitments.