both of you can get married. that in itself will not confer status to him. you will need to petition for him I-130, and he can at same time apply for adjustment of status. assuming no grounds of inadmissibility, he ought to be okay.
I concur with my colleague. Once you are married, you will need to file an I-130, Petition for Alien Relative, and and I-485, Application for Adjustment of Status. They can be filed concurrently. As your boyfriend entered the U.S. legally, he is eligible for adjustment of status in the U.S., again assuming no bars or grounds of inadmissibility (which are usually convictions). In Phoenix the process takes approximately four months, but other offices may work within a different time frame.
Best of Luck.
Deniz S. Arik, Esq.
The Law Office of Deniz S. Arik, PLLC
2942 North 24th St.
Phoenix, AZ 85016
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