A fee was agreed for the 22-year-old midfielder around two weeks ago but Clingan only yesterday signed a two-and-a-half year deal at the City Ground.
He told the club website: "I was delighted when Forest had a bid accepted for me but I was in the last year of my contract with Wolves and wanted to establish what their plans for me were.
"I may have left a Championship club," commented the Northern Ireland Under-21 international, "but I don't regard this as a step down. It's a massive career move for me."