The midfielder has top-level experience having played for Chile at the 2010 World Cup and the club's confirmation that his fee is a record one means he has cost more than the £8million they recently paid to Tottenham for Steven Caulker.
"We're delighted to have secured the services of Gary - a tenacious and intelligent international midfielder," manager Malky Mackay told his club's official website.
"Having had two seasons of regular football in La Liga - with 60-odd international caps to his name and three appearances at a World Cup - his experience will be an invaluable asset to our squad.
"He's played in a number of Boca v River Plate derbies in Argentina - one of the world's biggest derby matches - and I've no doubt that his background and pedigree will complement our midfield group in the Barclays Premier League."
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