Yes- it seems you are eligible. To claim an older child as a dependent, you need to meet all of these tests:
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Not a qualifying child test, Yes, he's too old to count for this test
Member of household or relationship test, Yes, he is both related to you and lived with you.
Gross income test, and He needs to have made less than $4050 for 2016
Support test. You need to have provided over half of his support for the year
Based on how you worded your question, it seems you can claim him as a dependent.
https://www.irs.gov/uac/who-can-i-claim-as-a-dependent
