Transfer my iPhone to new computer

Hey,guys! I am confused about transfering iPhone to computer.
What I need help with is transferring my iPhone backup (and whatever else is needed) over to the new computer.
I get how to transfer my music: consolidate library then move the iTunes library over to the new computer and replace the iTunes library.
But what do I need to do for the iPhone? I know there is a backup for it somewhere that I need to move but don't know where it is. If you nice guys can give me a free recommandation program to do that?
Thank you!

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Surely you can just connect your iphone to the new computer and create a new backup within itunes by right clicking on your iphone under "Devices" and then select "Back up" from the menu that appears.
Moreover,i share you two articles about iPhone to computer:
For PC: How to transer or backup iPhone contents to PC
For Mac: How to transfer or backup iPhone contents to Mac
Hope them can do you a favor.

no way

If you're not jailbroken, you don't really need your last backup. Just plug in to itunes on the new computer as soon as you get it and sync. New backup created.

When I transferred it between my PC and Mac, I plug it in and right click the iPhone and "transfer from iPhone".

Another alternative which I did was plugged in an external hard drive, and manually selected all my purchases from the user\music\iTunes folder and dragged the iTunes folder with the sub info to an external drive and then select the folder again and move it from the drive to the new computer in the same location it was
(Windows: My Documents folder\music\iTunes)
(Mac: Accountname\Music\iTunes)

Note: For all purchase accounts, you need to authenticate. I have two accounts (gmail and me) which is troublesome. I have yet to find out how to change the email address properly from gmail to the me account since the account already exists.

There is good software called Aiseesoft iPhone transfer it works great and available both for Mac and Windows

you can use iphone to pc transfer to copy all your iphone files and apps to your computer. It's easy and simple. I have used a iphone transfer software.

iTunes can transfer data from the iphone to the MAC. the problem is you do not want to use iTunes ?