The 29-year-old central defender signed a three-year deal after a fee of £350,000 was agreed with Premiership new-boys Wigan.
Breckin told the official club website: "I know I am dropping down but I don't think Forest will be in League One for very long.
"The size of the club and the quality of the manager and the playing staff means that i hope we would be in the forefront of next season's promotion issue."
Breckin began his career with Rotherham before moving to Chesterfield.
He joined Wigan in July 2002, making 105 appearances for the Latics.