The 34-year-old, who was a free agent after leaving Inter, joins the Premier League newcomers on a one-year contract.
Cambiasso spent a decade with Inter and was part of the side that won the Champions League under Jose Mourinho in 2010.
Once part of the famous Real Madrid squad featuring Zinedine Zidane, Luis Figo and David Beckham, Cambiasso has been capped by Argentina more than 50 times.
He is known for one of the most memorable World Cup goals in recent times - scored for Argentina against Serbia and Montenegro in 2006 after a 25-pass move.
Cambiasso will wear the No 19 shirt at Leicester and could make his debut against Arsenal this weekend.
Watch Leicester v Arsenal live on Sky Sports 1 this Sunday, kick-off 4pm