The striker completed his loan switch to the Reds' Championship rivals on Wednesday afternoon and will remain at Oakwell until January 3, 2013. The move is with a view to a permanent transfer to the south Yorkshire club.
Tudgay has been limited to just two appearances for Forest this season.
O'Driscoll told the club's official website: "Marcus is an excellent professional and great to have around the place.
"But, understandably, he wants to be playing on a regular basis and that's something we cannot guarantee him. I'm sure it will be successful."