Think of changing your website URL like moving the physical location of your store or office. It's possible, but requires preparation and a fair bit of work. Here's the steps you'll need to take:
Change your address
NiceJob does most of the work for the first step. You provide us with the new URL that you already own, and we change your Zone File to make sure traffic keeps flowing smoothly. As Google does use domain history as a ranking signal, changing your domain may negatively affect your ranking.
To avoid losing all the existing traffic you have, you'll need to create 301 redirects for all you old pages pointing to your new site. There's a few methods of doing this, you can get an overview here.
Register move with webmaster tools
You'll need to tell Google your website has moved, and you can do that using webmaster tools. You can get more details here.
Change all your website citations
This takes more time. Even though you've put your re-directs in place, you'll want to change all your existing website citations to your new URL. This includes company pages like Facebook, Twitter, Google+, LinkedIN, Yelp, Angies List, major directories, etc.
Because of the amount of work required to properly change a URL, we recommend that you only do it if you have a real reason for it.