transfer ios backups to new computer

I'm replacing my mid-2010 MBP with a new MBA and have a quick question. I backed up all my media to an external hard drive, but want to avoid the dreaded "This iPhone has been synced with another itunes library" message that would precede the erasing of my phone if I wanted to sync it to the new computer. How do I make it so the phone recognizes the new computer as the same library?

I've been reading about making a disk image to just mirror the installation of my current mbp, but would like to copy the backups over to the new computer, or just make it so the new computer is recognized as the same library so I can sync without issues.

I understand the other option is a fresh install altogether, but want to avoid it if possible so I don't lose the iPhone/iPod/iPad backups, or have to wait the ungodly amount of time that it would take to sync every iOS device I own like it did when I restored my iPhone 5 from an existing iPhone 4 backup.

Any ideas?

Macman45 said:

MA is the best bet. You can use wifi, ethernet or T/Bolt cables to connect the two Macs...Follow the steps on the screen and your new Mac will be the same as your old one. ( As lonfg as they are running the version of OSX )

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I'd never heard of Migration Assistant, just googled it now. I assume that's the way that the Apple Store people will be transferring all the files from one to the other when I go in a week from today and pick it up? I added One to One if for nothing else than to make that transition seamless. Even if they don't do it, from what I'm reading, Migration Assistant seems like an easy option. My current MBP has Mountain Lion on it so the Operating Systems should be the same on both computers.

apollo1444 said:

it is very easy to do it you don't need to go to an apple store, its already installed in your computer have you tried looking for that as well? lol

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I'd never even heard about Migration Assistant before yesterday, sounds like exactly the tool I need to do this. It's like Apple has done this before.