Cardiff will allow long-serving Kevin McNaughton to leave this summer along with Danny Gabbidon and Nicky Maynard.
Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
As revealed on Friday, Forest were poised to sign Gillett on a free transfer after he impressed on trial.
Gillett left Doncaster earlier this summer upon the expiration of his contract at the Keepmoat Stadium.
The 26-year-old has penned a two-year deal at the City Ground after being reunited with former Rovers boss Sean O'Driscoll.
Gillett is Forest's fifth signing of the summer and Forest chairman Omar Al Hasawi was delighted to land the midfielder.
"Simon is a player that Sean knows well from his Doncaster days and we are delighted to welcome him to the club," Al Hasawi told the club's official website.