It is legit for him to claim a dependent if the divorce agreement specifically stipulates he can and he supports the dependent in some way.

For you to have the deduction to yourself, you either need to get the divorce agreement amended or forgo support. There's really no basis for an amendment unless you ex voluntarily agrees to one.

Before getting much more worked up about it, I suggest you ask your accountant to run your taxes with and without a dependent and get some perspective on what this is costing you.