Munoz's arrival at the City Ground follows two and a half trophy-laden years in south London, during which he racked up 109 appearances and 11 goals for Crystal Palace.
The move makes him Nottingham Forest's second major addition of the closing window, arriving on a three-year contract shortly after the club shattered its transfer record to land Liam Delap for £50m - with Saturday's visit of Tottenham Hotspur a realistic target for his debut.
"I'm really excited because I can see so much talent, Forest is a team with great players, great qualities and great skills on the pitch, I can't wait to get out there so I can help my new team-mates and I think that we're going to do great things," the 51-cap international said.
He pointed to the club's recent European run as a specific draw.
"It is a club that's fought hard in recent years, it has competed hard, it got to the semi-finals of the Europa League and I think it has even greater objectives for the future, and really this is what I like about Forest, and that's why I decided to come here."
Forest's chief football officer, George Syrianos, said the club's recruitment team had tracked Munoz's performances closely before finalising the deal.
"Daniel has performed strongly in the Premier League and in European competition, and we believe he has the mentality and ambition to make a significant contribution to the club," Syrianos said.
The signing gives Oliver Glasner a wing-back with an intimate understanding of the system he wants to play, having filled the same role for the Austrian throughout Palace's trophy-laden 2025-26 campaign.
The move continues an active window at the City Ground, with the club already having strengthened significantly in defence and attack as Glasner reshapes the squad around players he trusts from his time at Selhurst Park.
Munoz's arrival is likely to push existing options such as Nicolo Savona further down the pecking order, and comes at a moment when Forest are also finalising Omari Hutchinson's exit to AC Milan, underlining the scale of turnover in Glasner's squad this summer after Everton's supporters forced the club to abandon an earlier attempt to sign Harrison Armstrong.