The 36-year-old, promoted from the youth team in March to replace the sacked Claudio Ranieri, oversaw a mini-revival at the 2010 European Champions but they still missed out on Champions League football by finishing sixth in Serie A.
Moratti has long admired former Barcelona coach Pep Guardiola but with the Spaniard taking time out of the game to recharge his batteries, Stramaccioni has been rewarded for his youthful exuberance.
"Yes, his contract was renewed earlier for three years," Moratti told reporters.
Stramaccioni had no previous top-flight managerial experience. A former Bologna player whose career was halted early by injury, he had only been Inter's youth coach for less than a year having joined from a similar role at AS Roma.
Inter's troubles last term were blamed by many pundits on their ageing team who were a pale shadow of the treble-winning outfit of 2010.
Moratti hopes Stramaccioni can blood some of the Inter youth squad, who won the Under-21 Next Gen European Championships in March, in the first team.
Inter are also recruiting from outside with Genoa forward Rodrigo Palacio on his way to the San Siro and Napoli striker Ezequiel Lavezzi a target.
"We said that we'd be in touch, but neither of us has been able to as we've both been busy," Moratti said when asked if he had spoken with Napoli president Aurelio De Laurentiis about the Argentine.
Moratti also reckoned Italy's latest match-fixing and betting scandal, where players have been arrested and Juventus coach Antonio Conte has been put under investigation, was less severe than the 2006 scandal in which referees were involved.
"It depends on how you see things, they're both unpleasant. The 2006 one came from high ranking officials and in my mind was even worse," he said.
