Described as a "left-footed Fernandinho" the energetic Brazilian will provide competition for Nemanja Matic and Paul Pogba in midfield after the retirement of Michael Carrick and expected exit of Marouane Fellaini.
After two seasons at Internacional, Fred joined Shakhtar in 2013.
Manchester United have officially announced the signing of Fred Rodrigues from Shakhtar Donetsk on a five-year deal.
A Mercedes van understood to be carrying Fred was pictured arriving at the Red Devils' HQ on Monday morning.
Asked whether 25-year-old Fred can make an impact at Old Trafford, Willian replied: 'Of course, no doubt about that.
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"He has a lot of quality, he can improve a lot".
Which team are you supporting in the 2018 World Cup?
United are also severely undermanned of elite defenders, having had to slot in makeshift midfielders of the likes of Ashley Young and Antonio Valencia at their full-back positions over the last several seasons. City were in the running to sign him but dropped their interest in January and have targeted Napoli's Brazilian-turned-Italian Jorginho instead.
"He's excited to start but now it's time to think about the World Cup and think about the national team".
The 29-year-old, who has scored eight times in 55 global appearances, felt last season was a good one personally but was coy about his plans after the summer.