Boro have beaten off rival interest from Celtic to land McGree, 23, who recently returned to MLS outfit Charlotte FC after a loan spell in England with Birmingham City.
He has now been officially announced as a Boro player ahead of the weekend's Championship game with Reading.
McGree's addition has followed on from the signings of Flo Balogun, Aaron Connolly and Bryant Akono Bilongo in what has been a busy first half of the transfer window for the Teessiders.
Meanwhile, in separate developments, squad players Uche Ikpeazu, Marcus Browne and James Lea-Siliki have all been made available for transfer, while another in Onel Hernandez has returned to parent club Norwich City and been loaned straight back out to Birmingham City.
Manager Chris Wilder had earlier confirmed that Browne, who is back to fitness after recovering from an ACL knee injury last January and Hernandez were in talks with clubs about moves.
Browne has been linked with Sheffield United.
Hernandez joined Boro on loan from Norwich City last August. His game time has largely come from the bench under Wilder, who allowed the 28-year-old to explore other opportunities as the Riverside chief plots more business in the January window and seeks to balance the books from a financial perspective.
Midfielder Lea-Siliki has failed to make an impact since joining on loan from Rennes, while Ikpeazu has had to largely settle for cameos from the bench since the arrival of Wilder.
The big striker - signed by former boss Neil Warnock last summer - has been linked with a return to old club Wycombe Wanderers, with Millwall having also been credited with interest.
Wilder said: “There are certain players that have been made available.
“Big Uche has been made available for loan and permanent transfer. His personality is fabulous.
“I think for maybe other styles and other systems, he would be suited but the way we want to play, and I’ve been open and honest with him, his game time is going to be very minimal. In terms of balancing the books, we’ve made him available.
“Marcus Browne is in talks with a couple of clubs on a permanent move. James Lea-Siliki has been informed that he’s available as well because of Riley coming into the group and Onel Hernandez is in talks with a couple of clubs.
“Onel has been great for me. Same as Uche, great attitude but he’s a wide player. He plays in a 4-2-3-1, he plays 4-3-3, he plays in a 3-4-3 as a wide player. He’s done a job for us down the middle and he’s give it a right go.
“I’ve got to say for a lad who’s come on loan and we’re making this decision, he’s one of the best pros I’ve worked with. He’s been a joy to work with. He’s another one and from a financial point of view, it’s quite a big number for what we are paying for somebody with game time now at the top of the pitch will be limited."
Meanwhile, left-back Neil Taylor has signed a new contract extension.