Gunnarsson, 27, played for Stoke City last season but left the club after his contract expired this summer.
Forest manager Paul Hart obviously saw enough of him in the pre-season games to award him with a contract.
The signing comes days after the proposed deal to purchase Leicester City midfielder Matt Jones fell through. Jones has now suffered more injury heartache after getting injured in Forest's 3-3 draw with Scunthorpe.
Jones has been out for around nine months with cruciate ligament damage and now faces a further four months on the sidelines with a back problem.