A statement from the club's website, manutd.com read, "Manchester United is delighted to announce it has reached agreement with Shakhtar Donetsk for the transfer of Frederico Rodrigues de Paula Santos (Fred)".
"A further announcement will be made in due course".
Pogba, who rejoined the Red Devils from Juventus back in 2016, will be hoping to help Manchester United mount a serious Premier League title challenge next season as they bid to try and beat Manchester City to the title.
Mourinho made signing a central midfielder his top priority this summer after Michael Carrick's decision to retire.
There are good reasons why Fred, who could make his World Cup debut against Switzerland, has gone under the radar, as Brazilian journalist Alex Sabino points out.
"If you sign Cristiano Ronaldo, do you tell him to track back all day and play a cautious midfield role?". Though the league brought to prominence the likes of Willian, Henrikh Mkhitaryan and Fernandinho, the level isn't exactly the strongest and a direct move to the Premier League might take some time to adjust to.
Fred was also part of the side which became the first team to defeat Manchester City last season, helping Shakhtar qualify for a last-16 game against Roma.
Handed his debut by Dunga in 2014, Fred's global career was disrupted after testing positive for the diuretic hydrochlorothiazide during the 2015 Copa America.
"It's very hard, I don't want to be emotional but I have to be", the Portuguese coach told RT.
"You will have to see with him".
The Brazil squad, now preparing for Sunday's friendly against Austria at Tottenham's Enfield Centre, were quick to congratulate Fred on Tuesday after his move was confirmed.