Ok. You should wait a little while. Why? Because you do not want him to be slapped with visa fraud. I'll explain. The regulations state this:
If a person does anything to make their status permanent in the U.S. (such as marrying a U.S. Citizen) within 30 days of entering on a non-immigrant visa
such as a tourist visa or an ESTA Visa Waiver, they are automatically charged with visa fraud.
If a person does anything to make their status permanent in the U.S. more than 30 days after entering on a non-immigrant visa but less than 60 days, they will be questioned extensively and if ICE or USCIS is not satisfied, then that person will be charged with visa fraud.
If a person does anything to make their status permanent in the U.S. more than 60 days after entering on a non-immigrant visa, no questions are asked because the policy determination is that it is too difficult to prove that the person did not just change their minds.
So he should wait until 60 days or more have passed then he entered the U.S., then you can marry and file the following forms so that he does not have to leave the U.S.:
I-130 (Petition for family member), I-485 (application for Lawful Permanent Residency), I-765 (Application for work permit), I-131 (Application for Advance Parole), G-325a (Biographic data - one for each of you), I-693 (Medical exam that a certified doctor must fill), and I-864 (Affidavit of support). You will need to file each form with supporting evidence and appropriate filing fees. You can find these forms at www.uscis.gov/forms.
The supporting evidence that you would file would be birth certificates, marriage certificate, divorce certificates if either of you have been married previously, proof of your U.S. Citizenship, proof of your spouse's legal entry into the U.S., and financial documents to prove your income over the last year at least.
In about 3 to 5 months after filing, he should get a work permit. About 5 to 7 months after filing you should get a marriage interview. If all goes well, a few weeks later he should get a Residency status (green card).
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