The 25-year-old Brazilian midfielder is waiting for the UK government to issue a work permit and the understanding at Old Trafford is that this will happen in the next few days.
A fee of more than £50m was agreed earlier this month for the Brazil international who is in Russia for the World Cup finals.
United fought off interest from Premier League champions Manchester City to land a long-standing transfer target.
Fred starred for Shakhtar as they progressed to the Round of Sixteen where they lost to Roma on the away goals rule. The Brazilian scored in the first leg, giving the Ukrainians a slender 2 – 1 lead.
He began his career with Internacional for whom he made 55 appearances before moving to Donetsk in 2013. Since arriving in Ukraine, he played more than 150 games, scoring 14 goals.
His international career was interrupted by a two-year drugs ban between 2015 and 2017 after testing positive for a banned diuretic. He has been eligible for Brazil since July 2017 and added two more caps to the six previously won. He has yet to score an international goal.
Fred is the second signing of the close-season for United, following Portugal defender Diogo Dalot into Old Trafford.