According to reports in Holland, the 23-year-old left-back has flown to England to undergo a medical with United on Monday ahead of penning a five-year contract.
Buttner was quoted as saying in Omroep Gelderland: "This is truly a dream come true. It all went very quickly and I am of course very happy."
Neither United or Vitesse have made any official announcement regarding Buttner.
Buttner has been regularly linked with a move to England this summer and had looked poised to join Southampton with Vitesse announcing in July they had agreed a deal with the Barclays Premier League newcomers, but that switch fell through.
Buttner, who can also operate at right-back, came through the youth system at Vitesse.
The Doetinchem-born player made 107 appearances for the Dutch club and was named in Holland's provisional 36-man squad for Euro 2012, although he did not eventually go to the finals.