The 22-year-old was allowed to leave Loftus Road on Thursday despite being the club's leading scorer with 12 goals, seven more than nearest challenger Heidar Helguson.
The move was even more surprising as Helguson is out injured leaving Rangers boss Paulo Sousa with just one fit striker in Samuel Di Carmine.
"I was a bit surprised that I was allowed to go," Blackstock told Forest's official website. "Especially with Heidar out for the season.
"It was a bit of a surprise for me but then again it was an opportunity for me to come to such a big club.
"It wasn't going stale at QPR, I was far and away their top scorer on 12 goals and I thought I was having a decent season."