I had intended on giving two weeks notice to my employer (of 61/2 yrs) but had a personal situation so I ended up giving immediate notice that I was leaving. My employer called my new employer because they were already upset that I was going to work for them. My new employer was the designer of the software I supported for a school in AZ. My contract for the school was up in three weeks. My new employer called me on this before I started but after I had signed a contract to work. I then was let go after four and a-half months even though I was doing a good job, they told me I was not a good fit. I had just gotten an email from my boss two weeks before saying I was doing a good job. Is this legal for my former employer to call my new employer?

Is this legal for my former employer to call my new employer?

Certainly it's legal. You admit that what your former employer said about you is true, so there's really no recourse for you. And from your description it seems that your new employer received the call from the old employer 4-1/2 months before letting you go, so there doesn't appear to be a direct connection.

Yes they can and they can say or tell them anything that is true.

If you lied to the new company or told them that you had given notice, that will be one issue.

Also if you have a contract for employment with the new company, they can not fire you for any reason not within the contract.

** A side note of course if you sue the new company for firing you and even win, that fact that you sued them will be public knowledge and can also effect future employment other places.

It appears you went to work for a company that was supplying to the business you were working at.
Always tough, remember that old place is a customer of the new place, so if they are unhappy, it can effect you.