Nicolas Anelka is free to resume his career in England after completing an education course following his quenelle gesture.
St Mirren have signed winger James Dayton from Oldham on loan until the end of the season.
The 27-year-old Poland international has made over 140 appearances for Forest since arriving in the summer of 2009.
Terriers boss Mark Robins said: "We have made it clear throughout the close season that we would stay patient during the transfer window and today (Tuesday) that patience has paid dividends with the arrival of Radoslaw.
"He is a top-class Championship player, especially in the number 10 role, and we're delighted to bring him to the club."