"I'm a romantic," Leonardo told his first news conference at Inter's training ground having arrived to wild applause.
"I wasn't looking for work, I was looking for a dream and this is the biggest challenge there is."
The Brazilian left Milan in May after his only season in management following a series of disagreements with owner Silvio Berlusconi.
He has returned to Serie A with Milan's biggest rivals having replaced Benitez but said his acceptance of the role was not the start of a vendetta against the Rossoneri.
"I thank Milan for 13 years together and I will never forget them but now I start a new adventure. I am a free man."
The 41-year-old World Cup winner was a player for Milan before becoming a scout, technical director and coach, making his switch to their bitter rivals all the more surprising.
However, the clubs have often swapped personnel over the years and league leaders Milan have stayed largely quiet on the issue given their hopes of silverware this term rely on former Inter striker Zlatan Ibrahimovic.
Inter are bidding for a sixth straight Serie A title but lie seventh at the mid-season break following an injury crisis and loss of confidence under Benitez.
"I still believe in the scudetto. I know 13 points is a lot but the championship still has a long way to run," added Leonardo, whose first game in charge is the January 6 clash with Napoli at the familiar San Siro.
Inter president Massimo Moratti is prepared for flak from Inter fans if his appointment of a former Milan coach, who only guided the Rossoneri to third last term, backfires.
"I am very happy about this appointment, I have always rated him," Moratti said of a man who speaks five languages.
"Now let him work without pressure but with all the ambition that we must have as champions of the world. He bears a heavy weight on his shoulders, as I do, for the decision the club have taken."
