United confirmed they had signed Colombian striker Falcao on a one-year loan deal from Monaco after the transfer window closed on Monday.
United completed the signing of versatile Netherlands international Daley Blind from Ajax on Monday for 14 million pounds.
Arsenal confirmed they had signed England forward Danny Welbeck to a long-term deal from Premier League rivals Manchester United as the transfer window closed on Monday.
United dominated Europe's transfer activity as the transfer deadline window slammed shut on Monday, Van Gaal taking his summer spending spree to more than 150 million pounds.
Van Gaal appears to be ignoring the burning issue of a porous and inexperienced back line which has struggled badly in the first three games of the season.
Real have moved to broaden their options in attack by agreeing to sign Mexico striker Hernandez on loan from United for the 2014-15 season.
Falcao is set to join Manchester United on loan after the Premier League club agreed to a loan deal with Monaco, a person with knowledge of the deal said on Monday.
Transfer deadline day takes centre stage as teams are given a final chance to add to their squads before the transfer window closes until January.
Borussia Dortmund re-signed Kagawa from United on Sunday to end the Japan midfielder's frustrating two-year spell in the Premier League.
Blind, who has 19 caps, made his first team debut in 2008 aged 18 and played almost 150 matches for Ajax Amsterdam.
For the Argentine midfielder, who was a Champions League winner with Real last season, his Premier League debut was a reality check.