This season I had written off because I never really got going at Middlesbrough
Boyd, who was signed by previous boss Gordon Strachan, had been linked with a move in the January transfer window and has not started a game since 5 February.
His arrival at Middlesbrough in July was seen as being a key signing in the Teessiders' promotion push.
Boyd netted 26 times as Rangers won the Scottish Premier League title last season and in doing so overhauled Henrik Larsson's SPL scoring record of 158 goals to end his spell as the league's top all-time scorer with 164.
However, a return of six goals from 29 appearances has been a disappointment, although Boro's collective poor form and the departure of Strachan has been a factor in his struggle to settle in the Championship.
But Boyd is relishing the chance to bolster Forest's promotion bid after his brief Boro spell.
"This season I had written off because I never really got going at Middlesbrough," Boyd told BBC Radio Nottingham.
"Hopefully this will be a new start and I can help Forest get promoted.
"The most important things is to play well and help the team get promoted. I'm delighted to be on board and hopefully we're all smiling at the end of the season."
Boyd is available for Forest's game away against Sheffield United on Tuesday.
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