If he claimed his own exemption on his tax return, you cannot claim him as a dependent. If he has already filed his return, for you to claim him as a dependent, he would need to file an amended return and claim that he can be claimed as a dependent on his parents return.
You do not need to wait until his amended return is fully processed, to claim him on your return. But, you cannot e-file. You will have to mail in a paper return.
He should not file his amendment until he receives his first refund.
Requirements to claim your child as a dependent:
1. he is a full-time student under 24 for at least 5 calendar months of the year (graduating in May usually means you meet the 5-month rule)
2. did not provide more than 1/2 his own support
3. lived with the parent (or was away at school) for more than half the year