Does he have to leave the country and go back to Singapore where he is a permanent resident and wait for the petition?

Your boyfriend has to get a divorce, first. If he does not, your marriage will be illegal under the U.S. laws, and, when USCIS finds it out (and they almost always do!),, there will be no end of trouble for both of you. After that, you can get married - in any jurisdiction that would register your marriage. Only after these two steps, your boyfriend can apply for an H4 visa. If, at the time of the application, he will be outside of the U.S., he will have to wait for a consular interview. If you get married in the U.S., the application to change status from to H4 can be filed and processed in the U.S. without the need for him to leave the country. However, there are certain precautions that have to be taken; so, if your boyfriend intends to come to the U.S. to marry you, you should consult with an immigration attorney before he starts packing his bags.

If he is married, he cannot legally marry you.