Matt Cutss explains over at his blog how you can best move your website to a new host or IP address without having problems in Google.
He talks about five steps:
Step 1. Find a good web host and sign up for an account.
Step 2: Make a back-up of your site at the new webhost.
Step 3: Change DNS to point to your new web host.
Step 4: Wait for the DNS change to propagate through the net.
Step 5: Once you are sure people or Googlebots are fetching from the new webhost/IP address, you’re done. You can shut down the old site.