The 26-year-old Aranguiz, who won the Copa America with the national team last month, also reached South America's Copa Libertadores semi-final with Brazilian club Internacional.
"We worked towards this deal for a long time which did not become any easier after his outstanding performances both at the Copa as well as with his club," Leverkusen CEO Michael Schade said in a statement.
"At one stage we had even written the deal off. It also makes it that much better that we managed to beat a strong international competition."
Leverkusen, who finished fourth in the Bundesliga last season, are taking on Italy's Lazio in the Champions League playoffs next week for a place in the competition's group stage. The German league starts on Friday.
"The Bundesliga is one of the most attractive leagues in the world and Leverkusen are one of the top teams here for years," said Aranguiz. "My national team colleague Arturo Vidal (who joined Bayern Munich) was impressed by Leverkusen so I really wanted to come here. Plus I have the chance to play in the Champions League."
(Reporting by Karolos Grohmann; editing by Amlan Chakraborty)
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