The signing of Blind from Ajax, for a 14 million pounds fee, was confirmed on the Premier League club's website (www.manutd.com).
"Louis van Gaal is a tremendously talented coach, I have worked with him at Ajax and also for the Netherlands national team and I cannot wait to work with him at the biggest club in the world," Blind said of his new club manager.
Meanwhile, Falcao was in Manchester for a medical examination ahead of a proposed season-long loan from Monaco, a move which was revealed to Reuters earlier on Monday by a source close to the deal.
The 28-year-old scored 11 goals in 20 appearances for Monaco after joining from Atletico Madrid for a fee of around 50 million euros last year.
Falcao, who missed the World Cup after suffering a serious knee injury, had been linked with several top European clubs including Real Madrid.
He will compete with regular strikers captain Wayne Rooney and Dutchman Robin van Persie for a place in a reshaped United team.
In another deal, United released Mexico striker Javier Hernandez on a season-long loan to Real Madrid.
(Reporting By Michael Hann and Sam Holden,; editing by Amlan Chakraborty and Pritha Sarkar)
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