The 30-year-old was on the cusp of joining Forest in January 2013 but the switch collapsed at the 11th hour, angering the then-manager Alex McLeish.
Times have changed, however, and there were no hitches yesterday as Burke breezed through a medical before signing a two-year contract with Stuart Pearce's Sky Bet Championship club.
"There's no doubt that this is a Premier League club playing in the Championship," Burke said.
"I listened to what the manager had to say and what his ambitions are and I really liked what we spoke about. In the end it was a no-brainer for me."