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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.