The France international midfielder has put pen to paper on a four-year contract with the option to extend for a further year.
The 25-year-old made 253 appearances and scored 15 times for Southampton since his debut in 2008.
England Under-20 international Reed has bid Schneiderlin a fond farewell on Twitter and has highlighted the influence of the Frenchman on his career.
Best of luck to @SchneiderlinMo4! Learnt a lot from him, from cleaning his boots to playing & training alongside him, it's been a pleasure!— Harrison Reed (@HarrisonReed) July 13, 2015
Schneiderlin is one of the best midfielders in the Premier League, and he is certainly going to enhance the quality of United’s midfield.
The former Strasbourg star scored four goals and created 20 chances in 26 Premier League appearances for Southampton last season.
Schneiderlin had a pass accuracy of 89% and a shot accuracy of 43%, and won 43 headers, 16 dribbles and 79 tackles.