In wrapping up the deal, Cardiff City have smashed their transfer record for a third time this summer, having spent £8.5m on Steven Caulker after previously forking out £8m for Dane Andreas Cornelius.
After victory over Athletic Bilbao, Mackay revealed: "He was our guest here today.
"He was one of the top midfielders in La Liga last season and is an experienced international with more than 50 caps for Chile.
"He is a combative, defensive midfield player.
"We've been on the look out for a player like Gary for a while.
"His experience will be an invaluable asset to our squad."
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