The most natural way is, "I've got your back."
Though, if you're watching TV or listening to native speakers talk colloquially, you may hear, "I got you." OR "I've got you." - "I got you" is grammatically incorrect, but still, they're both common shortened versions. If you want to say the colloquial version, put the emphasis on the word "got". Like, "i GOT you." You can also use that phrase to mean, "I understand," but again, only in a colloquial way.
You will have my back. - Not correct. That sounds more like a command. Like, do or die.
I will back you up. - OK
You will be having me back up. - No
You will back me up. - It's correct as a command. You can put it as a question to soften it a bit, "You'll back me up?"