The Dutchman completed his move to Galatasaray yesterday.
"He gave so much to Inter," said Moratti. "And that's not purely sentiment, that's recognition.
"He'll always remain one of the key figures in Inter history. We're proud to have had him here and Galatasaray will be too."
Inter agreed his 7.5m sale some time ago, but the Dutch international refused to be rushed into making a switch.
"Am I happy with the end result? Yes, without a doubt," Moratti added. "Galatasaray did everything properly, their President, Vice-President, they're very good people.
"I think the player is happy too, otherwise he wouldn't have gone there.
"Why did it take so long? If something needs to happen, all that matters is that it does."