Cambiasso arrive in Milan on a free transfer after the Spanish giants decided against renewing his contract at El Santiago Bernebeu.
The South American has signed a four-year deal with the Nerazzurri, and will not take up a place as a foreigner as he holds an Italian passport.
Cambiasso has struggled to make a name for himself at Real with so many big stars playing alongside him, and will hope for better fortunes in Milan.
Cambiasso could be playing for a new manager at Inter, with the club in negotiations with Lazio to install Roberto Mancini as their new boss.
Mancini has been expected to take the post at Inter for some time, but he still has four years left on his current Lazio deal.
Both sides have claimed to have Mancini in the past, but Lazio seem to have resigned themselves to losing their manager and have opened talks with Inter.
"There has been a meeting between Inter and Lazio," said Nerazzurri president Giacinto Facchetti.
"The rapport of collaboration there has always been in these years continues.
"This is without doubt the most important thing. We have found a way to talk, and the rest will come."
