Moving iTunes to new Mac & iPhone sync

I just setup a new iMac (reinstalled all my apps) and moved my iTunes library to the new iMac...no problems. But I'm unclear as to what to do with my iPhone and iPad, since when plugged into the new iMac iTunes doesn't recognize them. I have the old Mac still running and on my network, so I can easily grab the old backup files for both, but wanted to know the correct order in which do do all this. Thanks for any suggestions.