The 18-year-old has established himself as a top talent after coming through Southampton's fabled academy.
Shaw has attracted admiring glances from many, including boyhood club Chelsea, but Press Association Sport understands it is United that have won the race for his signature.
The left-back underwent a medical at the club's Carrington training ground on Thursday evening ahead of a move worth £27million plus add-ons - a lofty price tag comes thanks to his fine performances for club and now country.
Despite not turning 19 until July 12, Shaw has already racked up 60 appearances in the Barclays Premier League and three England caps.
The full-back made his Three Lions debut in the friendly against Denmark in March and usurped idol Ashley Cole in Roy Hodgson's pecking order, leading the experienced left-back to call time on his international career.
The 18-year-old was one of few positive points from a miserable World Cup campaign and became the youngest player to feature at the tournament when he started Tuesday's goalless draw with Costa Rica.
After that match it was put to Shaw that he perhaps needed to be playing Champions League football to feel comfortable on the world stage.
That kind of experience would not come if he was to move to United this season - but was not something he deemed particularly important to being a success with England anyway.
"You can't really say that because you look at the other teams and they haven't all got Champions League players, have they?" Shaw said.
"I don't know. Obviously Champions League would help, playing against world-class players, but you can't just say that because you look at other teams that have gone through the groups and they haven't got all Champions League players."
Shaw will be competing with Patrice Evra for the left-back role at Old Trafford, but is understood to have been told he will be first choice despite competition from the France international.
Evra penned a one-year contract extension in May and last season's back-up Alexander Buttner looks set to move to Dinamo Moscow imminently, joining Rio Ferdinand and Nemanja Vidic in leaving as the club look to kick on after a miserable season.
United limped to a seventh-place finish last term, resulting in David Moyes losing his job and Holland coach Louis van Gaal coming in as his replacement.
Shaw will become the second major arrival since the Dutchman's appointment, following Ander Herrera's move from Athletic Bilbao on Thursday.
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