We've covered the major issues with moving a business within Google Maps a couple times - in short, it is a scary and upsetting thing to have to deal with - on top of all the other issues with Google Maps.
Google's Jade Wang finally gave official advice on what to do when you do move your business. She wrote in a Google Business Help thread:
Verified business owner of a page, and is your business moving locations? Here's what you do.
Edit your address in Google Places for Business or in the Google+ page admin area, whichever you are using to manage the page. This will either make a new page or edit the address on the existing page. It may take a week or two after editing your address before you see an update. At this point, you may need to go through a verification process again. Don't worry -- this is normal.
If you see a page that's still got the old address, click on Report a problem and mark that location as closed. Provide the link to the new address or information about the new location if possible. You can find more instructions on closing a location here: http://goo.gl/YZIjq
I actually took these steps for my business and it did create two listings. But I do not want to mark my old listing as "closed" because my old listing still is the number one result. I do not want my business to appear as if we closed down.
Forum discussion at Google Business Help.