The Southampton youngster is set to complete his transfer to Old Trafford, just a day after the club sealed the signing of Athletic Bilbao star Ander Herrera
The Southampton defender arrived at United's training ground Carrington via a back road around midday on Friday, having completed most of his assessments off-site on Thursday evening and Friday morning, to be met by club officials and be given a tour of the facilities.
The left back has agreed terms on a deal worth 160,000 pound-a-week that will make him the highest-paid teenager in world football.
Shaw will become the second signing of new manager Louis van Gaal's reign, following the acquisition of Ander Herrera from Athletic Bilbao on Thursday.
United has long been admirers of the England international defender, and had to fight off interest from both Chelsea and Manchester City to secure his signature.
The club had hoped to complete the transfer before the World Cup but was hindered by Southampton's own pursuit of a new manager - a role finally filled by Ronald Koeman earlier this month, following Mauricio Pochettino's departure for Tottenham.
Shaw played for England at the Samba showpiece in the match against Costa Rica, and is expected to enjoy a more prominent role in the England team in the coming years, with veteran Ashley Cole having retired.
In the Premier League, meanwhile, Shaw featured 35 times for an exciting Southampton team in 2013-14, contributing two assists.