The goalkeeper, 20, was available after being released by Oxford United last season.
Plumley failed to make a single senior appearance for the League One side while taking in loans at Beaconsfield and Weston-super-Mare.
And he becomes United’s eighth transfer signing of the summer under Erik ten Hag.
Plumley is a boyhood United fan and will now link up with United’s youth sides after being registered as an eligible U21 player.
The Red Devils have seen a flurry of movement between the sticks this summer.
Stalwart David de Gea was shown the door when his contract expired.
And back-up Jack Butland was allowed to join Rangers on a free transfer.
Dean Henderson also completed a late move away from Old Trafford to Crystal Palace.
Meanwhile, there were exits for youngsters Nathan Bishop and Matej Kovar too.
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United reinforced with Inter Milan’s Andre Onana and Fenerbahce’s Altay Bayindir for a combined £60million, making it three goalies signed in the most recent window.
Elsewhere, United boosted their attack with Chelsea’s Mason Mount and Atalanta’s Rasmus Hojlund.
Their defence now also boasts Jonny Evans and Tottenham loanee Sergio Reguilon.
And midfielder Sofyan Amrabat was also signed for the season from Fiorentina.
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