I did this. I was on H1B and wife is American. For starters, you don't have to leave the country for anything. You and your wife will apply for Green card and Change of status. But this is after marriage.
You actually can't leave the country after filing for the GC, unless you get a special travel waiver (or your GC request will be considered abandoned).
Anyone in this situation is strongly encouraged to consult an immigration lawyer and spend the time to give them all the information you have, and listen to all the caveats they list. Yes, it will cost you a kilobuck, but potentially save you a lot more kilobucks, a lot of time and a lot of anxiety.
