The 26-year-old defensive midfielder flew to Wales after the Liga side's 3-1 win over Manchester United on Friday night and has agreed a four-year deal, subject to a work permit
Bluebirds manager Malky Mackay revealed earlier on Saturday that the 26-year-old was "95 perc cent there" in terms of signing for the newly-promoted Welsh side, and a deal has now been struck and the player has completed a medical.
Reports in Spain suggested Medel had flown directly to south Wales following his club's 3-1 win over Manchester United in Rio Ferdinand's testimonial, and following the Bluebirds' 2-1 win over Athletic Bilbao on Saturday afternoon, the club have confirmed they have broken their transfer record for a third time this summer.
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"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."
Medel said his goodbyes to the Andalusian club earlier in the day amidst speculation linking him to Cardiff, following reports that he would complete a medical ahead of a €13 million [£11.1m] move.
He told Orgullo de Nervion: "It's difficult for me. I want to give my thanks to Sevilla. I will always be with this team, until death.
"I'm going because it was a great opportunity for everybody, but it is complicated because of everything I feel for Sevilla."
The Chile international moved to the Liga club in January 2011 and has played 78 times for the Andalusians. Medel has a reputation for a combative style, receiving six red cards in his two-and-a-half years in Spain.