The 21-year-old centre-half has arrived at the City Ground on a five-year contract.
No fee has been disclosed but British media reported the deal to be worth £11.2 million plus add-ons.
Murillo is Forest's sixth signing of the summer transfer window, with the defender following Anthony Elanga, Ola Aina, Matt Turner, Gonzalo Montiel and Andrey Santos to the twice former European champions.
Murillo told Forest's website: "I am very excited to join Nottingham Forest.
"It is a big club with a huge fanbase and I cannot wait to start playing at The City Ground.
"The Premier League is the best league in the world, so I can't wait to test myself and give my all for this club."
Forest are away to Chelsea on Saturday, with manager Steve Cooper unable to say if club captain Joe Worrall would return to the side at Stamford Bridge following the death of his uncle, police officer Graham Saville, who was hit by a train last Thursday trying to help a distressed man on railway tracks.
The defender missed Wednesday's home League Cup defeat by Burnley through suspension after being sent off at Manchester United last week.
"Joe is dealing with the tragedy and we're supporting him as best as we can," Cooper said.
"We're here for him. Family comes first, football comes second."
