The highly-rated Croatian, 19, arrived from Dinamo Zagreb as Inter look to fill the gap left by the departure of Philippe Coutinho and Wesley Sneijder, who left for Liverpool and Galatasaray respectively.
The Nerazzurri also drafted in Stuttgart midfielder Zdravko Kuzmanovic and Atalanta winger Ezequiel Schelotto, but a move for Corinthians playmaker Paulinho broke down.
Moratti could not hide his true feelings when asked which of the trio he was most looking forward to watching at Siena on Sunday.
He told inter.it: "We've gone for players that we think suit the way we play.
"I think Kovacic is a particularly good signing - I think that he's a special player. He's very talented and very young, so he fits in with our plans perfectly.
"He's a special talent and he should be interesting to watch because I'm sure he'll give us something new and that's always nice.
"Football is beautiful when you see something you've never seen before."
Touching on Schelotto and Kuzmanovic, he added: "We needed a wide player and I think Schelotto fits in perfectly with what the coach was looking for.
"Kuzmanovic has a lot of experience even though he's still young."
Inter may be unbeaten in three matches but they have tasted victory just once in six attempts.
The club's injury crisis is easing, though, with only Luca Castellazzi, Walter Samuel, Dejan Stankovic and Gaby Mudingayi giving head coach Andrea Stramaccioni cause for concern.
Bottom side Siena's brief return to winning ways proved to be a false dawn as the Bianconeri returned empty-handed from Udinese.
A 1-0 victory over Sampdoria had put a stop to a run of six consecutive losses but a solitary Luis Muriel goal condemned Siena to a seventh defeat in eight.
Head coach Giuseppe Iachini said: "What can I say? Being satisfied with the overall performance is not enough.
"All it took were one or two mistakes in the midfield to ensure we went home with nothing. Sometimes football is like that."