Gunn, 29, has penned a one-year deal with Forest after coming off contract at Norwich City over the summer. Gunn made 35 Championship appearances for Norwich last season.
Gunn said: "I am really happy to be here. This is a historic Club on an exciting journey and I’m looking forward to being a part of it and getting to work.
"I’m joining a good group of keepers, and I believe my experience will add something to the team. I can’t wait to get going."
Chief Football Officer, Ross Wilson, added: “We are pleased to welcome Angus to Nottingham Forest today. He joins a strong goalkeeping department and adds his experience to the group.
"I know how much Matz has enjoyed his work with Rui Barbosa, and I’m sure Angus will enjoy that same coaching and support as he settles into the club."