Can my ex- husband claim me as a dependent because he gives me alimony and child support?

[DoninGA]

See this IRS work sheet for determining support - https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf

To claim someone as a dependent under the Qualifying Relative rules they have to meet all the requirements under the rules.

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,700 (social security does not count) in 2023
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.

[DoninGA]

Child support payments you receive cannot be used for determining support to a dependent.  It would be highly unlikely that the alimony you receive would constitute over one-half of your total support requirements.

[Mike9241]

assuming you were divorced at the end of the year for which he is trying to claim you then

to be a Qualifying Relative -

The person either (a) must be related to you or (b) must live with you all year as a member of your household.

this rule is not met if a) you were divorced at year-end because you are no longer related to him  

and 

b) you did not live with him for the entire year. 

you cannot stop him from claiming you. if he files before you do and claims you, you will not be able to e-file. You'll need to mail in your return. use a tracking method so you know the taxing authorities get it.  Eventually, the IRS will get around to making inquiries to both of you as to your dependency status. If you are due a refund, this can delay it and no telling when the issue will be sorted out. 

[rjs]

Support doesn't matter. Support is not the only requirement for claiming someone as a dependent. Your ex-husband cannot claim you as a dependent because, as Mike9241 pointed out, you do not satisfy the relationship test (item 2 in DoninGA's post above). Even if your ex provides all of your support, he can't claim you.