I think it would be a good idea to get the advice of an attorney on this one because there is conflicting information, some good, some not so good.
The bad side is that as your boyfriend has overstayed his visa, he could be subject to a ten year ban from the US. However, there is a waiver form (form 602) which could overturn that and make him a legal citizen because of marriage.
The fact that he entered the country legally is a good thing, you should be able to convince the authorities that he should be allowed to stay.
If you get married and can prove to the authorities that it is a real marriage and not just one of convenience, you can apply for an 'adjustment of Status'.
He should be granted a provisional green card that will entitle him to stay for two years. After the two years are up you will need to show again that your marriage is genuine, and he should then get a full green card.
However please be careful, even if he has applied for his green card, if he leaves the US for 180 days he could be banned from returning. This is where a lawyer will be able to help further, and can avoid any pitfalls or legal loopholes.
I hope it goes well, and I wish you a long and happy marriage :-)