Here's the answer from Google:
"Remove cached pages
Google automatically takes a "snapshot" of each page it crawls and archives it. This "cached" version allows a webpage to be retrieved for your end users if the original page is ever unavailable (due to temporary failure of the page's web server). The cached page appears to users exactly as it looked when Google last crawled it, and we display a message at the top of the page to indicate that it's a cached version. Users can access the cached version by choosing the "Cached" link on the search results page.
To prevent all search engines from showing a "Cached" link for your site, place this tag in the section of your page::
To allow other search engines to show a "Cached" link, preventing only Google from displaying one, use the following tag:
Note: this tag only removes the "Cached" link for the page. Google will continue to index the page and display a snippet.
Note: If you believe your request is urgent and cannot wait until the next time Google crawls your site, use our automatic URL removal system. In order for this automated process to work, the webmaster must first insert the appropriate meta tags into the page's HTML code."
The first solution removes cached pages from Yahoo as well. Should happen automatically the next time your site gets crawled.
If your url structure is different, however, I think what you're looking to do is set up a 301 redirect to permanently redirect old urls to new ones. In this case the cached urls could exist on Google (or wherever they were linked from), and the user would still be able to get to your site. This is a different question, however. Hopefully what's above answered the present one.
Best,
Bryson