Glasner, who delivered Palace their first major silverware by winning the FA Cup and UEFA Conference League in consecutive years, swapped Selhurst Park for the City Ground at the end of last season.
The 30-year-old Munoz, a key part of Palace's success under Glasner, has signed a three-year contract with the club holding an option for a further year.
"I think that Oliver Glasner is special, I have a very good relationship with him and we did big things together, it was an incredibly special period," Munoz told Forest's website.
"He's a tireless worker, he's a winner, and I think that's a part of the decision I've made - I know him and I know how he works, how his assistants are, and really they all have the same mentality and I'm on the same wavelength."
Munoz made 46 appearances in all competitions for Palace last season, including 29 in the Premier League, registering four goals and three assists.
He has also made 51 appearances for Colombia and was part of the squad for the 2026 World Cup.
"Daniel is a player who has consistently demonstrated his quality at the highest level, and we are delighted to bring him to Nottingham Forest," Forest's Chief Football Officer, George Syrianos, said.
Forest, who drew with Liverpool at the weekend after losing to Leeds United on the opening day of the Premier League season, could hand Munoz his debut against Tottenham Hotspur on Saturday.