Jose Mourinho revealed earlier today that Pereira was close to joining the Spanish side.
"I love Andreas Pereira as a player and I would love to have him in my squad," Mourinho said.
But the player is heading off to La Liga instead to get regular match action.
Granada have now confirmed the deal is done.
The club wrote in a statement: "The Granada CF has reached an agreement with Manchester United for the transfer of Andreas Pereira until June 30, 2017.
"He made 22 appearances in Premier League matches, Europa League, FA Cup and Champions League and reserve games last season.
"Pereira scored six goals and got three assists.
"The player will train with the team tomorrow and will be presented next week."
Pereira joins Chelsea's Jeremie Bogie and Victorien Angban and Arsenal's Jon Toral in joining Granada on loan.
