The 26-year-old has signed a four-year contract, subject to a work permit.
Medel completed his medical on Saturday after having featured for Sevilla in their 3-1 win at Manchester United on Friday.
Cardiff City manager Malky Mackay told the club’s official website: “We’re delighted to have secured the services of Gary – a tenacious and intelligent international midfielder.
“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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.