Depending on clearance, he may feature in the squad for United for their game against Aberdeen on Saturday.
The 19-year-old centre back has signed a three-year deal after impressing during a trial period with the club.
Manager Craig Levein said: "Although a centre back is not a top priority for us at present, I felt that Michael was too good an opportunity to miss."
He continued: "I'm delighted that he has agreed to join us on a permanent basis.
"He's only 19 and is therefore seen as one to develop for the future, but if he continues to impress, he may well feature in the first team this season."