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.
GEAR:Inter Milan strips available here with Kitbag. Free delivery on orders over £50
"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."
Leonardo failed to shine in his only season in management with Milan last term, leading the Rossoneri to third place in Serie A and the Champions League last 16.
The 41-year-old also played for Milan before becoming technical director there and has no prior links to Inter, making the decision to appoint him all the more strange to the hordes of baffled Tweeters and newspaper columnists.
"Unbelievable", "traitor" and "downright weird" were just some of the terms used on Twitter to describe the move.
BIG GAMBLE
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.
Giovanni Trapattoni famously managed Milan, Inter and the third Italian giant Juventus while Milan striker Zlatan Ibrahimovic has played for all three.
Indeed Milan have been the side most guilty of signing ex-Inter names with Ibrahimovic, Clarence Seedorf, Andrea Pirlo and former forward Ronaldo all having previously turned out for the Nerazzurri among others.
Moratti, whose side won an unprecedented treble last term under Jose Mourinho, is still taking a big gamble by naming Leonardo with fans likely to give him a little lukewarm reception at first.
Given Leonardo left Milan after a bust-up with owner Silvio Berlusconi, hands-on Moratti risks similar issues if Inter do not quickly start rising up from seventh in Serie A and lose to Bayern Munich in their Champions League first knockout round.
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.
On the other hand, pundits such as Gabriele Marcotti have argued that choosing L
