Really depends on how your redirects are set up. But you can check the status code using Firebug (or a comparable tool with a request profiler).
Open up the “net” tab in firebug, and hit one of your old URLs. You should** see the request show up at the top of the list, and you’ll see the response code in the “status” column. If your redirects are working correctly, the first request will have a status of 301, and will be immediately followed by a second request for your new url, with the status 200.
You coud also do this in Chrome developer tools. The tab you’d use there is titled “Network”.
** If your intial request disappears from the list, it probably means that the redirect is being done via JavaScript or some other non-legit method. This method of “redirection” is incapable of returning status codes like 301.