The 27-year-old Scotland international will spend the rest of the season at the City ground, with 31-year-old keeper Paul Smith travelling in the opposite direction.
Mowbray said: "It's a good deal for the club and it's a good deal for the player (Boyd), who will hopefully get some game time and build his confidence back up."
Boyd joined Boro from Rangers on a free transfer during the summer of last year with then manager Gordon Strachan believing he had pulled off something of a coup.
However, the goalscoring exploits which made the striker's name in his native country have largely deserted him on Teesside and his 29 appearances to date have seen him find the back of the next just six times.
But Boro's need for a keeper became Mowbray's major concern when Jason Steele tore a stomach muscle during Saturday's 5-2 defeat at Reading.