I migrated over the feeds from Feedburner to Google Feedburner. Everything seems to went well and hopefully there won’t be any problems. All you need is to signed into your Google Account, after which you try to sign into Feedburner and it will automatically offer to bind the Google account to your Feedburner account. Hopefully the old URL’s will all work (they seem to at the moment). Some useful links:
If you are using Feedburner, you might want to sign into your account to migrate over to Google (the deadline is AFAIK the 28th of February).
Image taken from dannysullivan's photostream with permission.