The 23-year-old centre-back joins Inter for an initial eight million euros transfer fee and put pen to paper on a five-year deal with the Nerazzurri club.
A statement from Inter read: “F.C. Internazionale is delighted to announce that it has completed the permanent signing of Jeison Murillo from Granada.
“The 23-year-old Colombian defender has signed a five-year contract with the Nerazzurri.
“The whole Inter family would like to give him a very warm welcome to the club.”
Serie A side Udinese brought Murillo to Europe five years ago from Deportivo Cali.
He was then sent straight on a season-long loan to Granada, who purchased his sporting rights in the summer of 2011.
The South American, who made 18 league appearances for Granada in the 2014/15 season, recently competed with Colombia at the Copa America in Chile.
Murillo’s goal gave Colombia a surprise 1-0 victory over Brazil in the group stages of the CONMEBOL competition.
Inter finished a disappointing eighth in Serie A last term and will not play in Europe this season.
However, the Nerazzurri have strengthened the squad since the end of the campaign with the arrival of Brazilian defender Joao Miranda from Atletico Madrid and French midfielder Geoffrey Kondogbia from Monaco.
Inter are also closing in on Spanish right-back Martin Montoya. The Barcelona player underwent a medical in Milan on Thursday, with the two clubs having reached an agreement for the 24-year-old to join the San Siro outfit on a two-year loan deal.