The 23-year-old has penned a four-and-a-half-year contract with the Serie A club after finalising his move from Spain.
"Udinese can announce the signing of Matias Daniel Campos Toro," a statement on the club's website read.
"The player has signed with the team a four-and-a-half-year deal, so his contract will run until June 30, 2017."
The Chile international had been on loan at Siena from the start of the season, but made just one substitute appearance in Serie A.
Campos joined Granada from Audax Italiano in January 2012, but was immediately loaned out to Universidad Catolica.
He was then loaned to Siena at the start of the new season, but failed to break into the starting line-up.