The 23-year-old has spent the season at Siena on-loan from Spanish side Granada - who, like Udinese, are owned by the Pozzo family.
"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."
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