Yes he would be adjustment eligible if his manner of entry into the country was legal and he is married to a US citizen in good faith. Consider consulting with an attorney for further guidance.
So generally, yes, a nonimmigrant who has been admitted to the US legally will later be adjustment eligible as an immediate relative of a US citizen spouse. However, there may be other issues to review about eligibility to adjust status or inadmissibilities, as appropriate. Seek private consult to review your particular circumstances.
You should retain an immigration lawyer to help you with this matter. You may search for one near you here on AVVO or at www.aila.org.
From the information provided, it does look like your boyfriend should be eligible to adjust. However, I do suggest talking to an attorney to screen for any complicating factors. We offer appointments by phone as well as in person.
This answer does not create an attorney-client relationship and is not meant to be relied upon as legal advice.
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