The 21-year-old will sign a five-year contract with the Eredivisie side next week.
“Negotiations with Universidad took a while, but were always in a friendly atmosphere,” Twente president Joop Munsterman said.
“We are very pleased that Gutierrez is joining Twente. He is a talented player who has developed into a Chile international.”
Twente has reportedly agreed to pay around €3million for the highly-rated midfielder.