The Ivorian becomes Mourinho’s first signing as Manchester United manager.
The defender was bought from Villarreal subject to a work permit and is believed to have cost around the region of £30m.
The 22 year old is going to be under pressure to help fix a very leaky Manchester United defence.
Bailly said about the transfer, “It is a dream come true to be joining Manchester United. To play football at the highest level is all I have ever wanted to do.”
The defender was part of the Ivory Coast team that won the nations cup and has played 40 times in the La Liga.
Manchester United remain in the pursuit of PSG striker Zlatan Ibrahimovic and hope to tie up that deal soon.