The 40-year-old defender received a rapturous reception when he entered the pitch in the 52nd minute of the game against Lazio, as goals from Mauro Icardi, Hernanes and two from Rodrigo Palacio earned the Nerazzurri a rousing 4-1 win.
Zanetti addressed the San Siro crowd after the game and the celebrations to mark the end of his time at the club, with whom he has won 16 trophies since joining from Banfield in 1995, continued at the Botinero restaurant, where Moratti made his revelation on the star's future.
"I had thought of a role as president," the 68-year-old told reporters. "But I know that he'll be vice-president, which I imagine is something prestigious for him.
"I'm glad this was thought up. It's up to him to do well in this role but he certainly will do because he has the right head for it."
Inter captain Zanetti has made 857 appearances for the club and is also Argentina's most-capped player having represented his nation 145 times - and Moratti was keen to express his affection for the player."I'm fond of all the guys who got the treble," the Italian continued at the restaurant co-owned by Zanetti and Esteban Cambiasso.
"Javier came five months after I took office. He has experienced the same emotions and stories as I have. I understand him.
"There is a special feeling for me and he has earned this sincere and spontaneous celebration."