Stuivenberg, who has given up his post at the helm of Netherlands Under-21s, starts the role of assistant coach at Old Trafford immediately.
With Louis van Gaal not currently at United as he leads Holland's charge in the FIFA World Cup, the 43-year-old is currently working alongside assistant manager Ryan Giggs.
Stuivenberg previously led Holland's Under-17s to UEFA European Championships wins in 2011 and 2012.
He is the fourth confirmed member of van Gaal's entourage alongside Giggs, Marcel Bout and Frans Hoek.
The futures of the likes of Nicky Butt and Phil Neville, who worked under David Moyes, have yet to be announced.