The 29-year-old, who played a key role in his country's run to the Copa America final this summer, ends a four-year spell with River Plate to join Jorge Sampaoli's side.
Sevilla has landed Argentina international Gabriel Mercado on a three-year deal, the club announced on Thursday.
Mercado links up with the Europa League champions after four seasons with River Plate in Argentina.
The 29-year-old won six trophies with the Buenos Aires club and was in the side that lost out to Barcelona in the 2015 Club World Cup final.
The defender is expected to help fill the void left by captain Coke, who departed the Primera Division side for Schalke in the Bundesliga this week.