The striker arrived at Middlesbrough last summer with an outstanding record of 101 goals in 143 games over four seasons at Rangers.
Yet Boyd failed to shine on Teesside and he will spend the rest of the season at the City Ground, with 31-year-old goalkeeper Paul Smith travelling in the opposite direction.
Boyd has yet to score in two appearances for Forest, but he said: "It has been difficult for me in England and I have heard all that about Scottish football, but I have a point to prove and I intend to do that.
"It's easy for people to give opinions, but a lot harder to go and do it. I didn't just score a few. It was a lot of goals so it wasn't a fluke.
"But there are better players than me who get criticised. It doesn't bother me. I'll get on with it and do my work on the football pitch."