Having seen the player at close quarters during his time as Bolton Wanderers manager, when Barrow underwent a trial spell with the Trotters, Freedman said he was 'all over' the opportunity to add the 22-year-old to his squad.
Barrow joined Swansea in the summer and has made an immediate impact at the Liberty Stadium, making seven Premier League appearances and earning a longer-term contract.
He joins Forest until the end of the season subject to international clearance.