The Brazilian succeeds Rafael Benitez, who left the world, European and Italian champions on Thursday after just six months in charge following a poor domestic spell and his public attack on Inter for not investing in new players.
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"Welcome, Leonardo is the coach of Inter," a statement said on Inter's website just hours after president Massimo Moratti had said there would be no announcement until December 27 at the earliest.
"A few minutes ago an agreement was signed which will tie him to the club until June 30, 2012."
"Unbelievable", "traitor" and "downright weird" were just some of the terms used on Twitter to describe the move.
Players and coaches switching allegiances between big rivals is nothing new in Italy, even if the idea of Arsenal's Arsene Wenger succeeding Manchester United's Alex Ferguson would bring howls of derision in England.
Spain is more similar to Italy with former Barcelona assistant coach Jose Mourinho now the Real Madrid boss while Portugal's Luis Figo signed for Real from Barca in 2000.
The appointment of Marcello Lippi in 1999 just after he had left rivals Juve was also disastrous for Inter and will prey on some fans' minds while Leonardo himself had indicated he wanted some time away from game to be with his family in Brazil.
