Now that I think about it, one of Zazu's best moments is where he doesn't say anything - where he watches as Simba makes his way up Pride Rock to reclaim the throne.
The atmosphere of the scene, combined with Zazu's amazed expression tells a lot in very little material. You can tell that the Pride looks on at Simba as a great gift that has come to save them all, but Zazu is slightly different in this case:
Timon and Pumbaa are the other non-lions around, but they are amazed that it's their Hakuna Matata pal who is now becoming king.
Zazu on the other hand, is not a lion, but at the same time, knew and went through the collapse of the Pride Lands under Scar's rule. Plus, as the majordomo, I wouldn't be surprised if under Scar, Zazu was the one forced to relay a few orders that only served to further ruin the kingdom. To top it all off, it was Zazu who often had to watch over Simba before the stampede.
The way I see it, Simba is not only a sign of salvation for the pride and the Pride Lands, but for Zazu, I think there was a little bit of the little bird's own soul that returned with the real lion king.