Will my music from my zune transfer to my ipod?

Sup, i have a zune and im getting an ipod for xmas. All of the music i have (witch is from cds i have and from limewire) shows up in my collection as soon as i download it and is easy to add to my zune with my zune software. So when i get my ipod and itunes will my collection be there just like on zune? will i have to download it all over again or is it even possible to put downloaded music on an ipod? id perferably like someone with both itunes and zune software experience to answer but anthing helps.