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If you can, do a global redirect in .htaccess from the old site to the new one. You need to do a permanent redirect (301) or the SE's will treat it as temporary. 301 tells them to change their records to reflect the new URI as the current page/site.
We've done this in the past, and since the site structure was the same, all the old pages redirected to the mirror new pages at the new site, i.e., www.mys*te.com/bluewidgets.html redirected to www.news*te.com/bluewidgets.html.
Another alternative might be to keep the existing pages for a while and add noindex/follow instructions for each old page to its counterpart at the new site.
Hope that helps. There's lots of info in here. Try searching on ".htaccess 301 redirect".
Here's a great thread on the topic too: [webmasterworld.com...]
Be prepared for some pages to vanish for a month or two while the SE's sort it all out. You may get lucky and see a smooth transition; you may not.