WordPress unfortunately does not work that way, you cannot simply create a page and 'redirect' the results there. The search results are always handler by the search.php file in your theme directory, which by default is triggered whenever the 's' query variable is set.
The only thing you can do is to change the site search URL to a 'nice url', and create a redirection rule for it via code, see this tutorial: http://wpengineer.com/2258/change-the-search-url-of-wordpress/
Then, you can enter the same custom url te search settings. I would only recommend doing the things in the tutorial if you have experience with .htaccess redirection rules, and I highly recommend having a full site back-up before doing any modification at all.Best,
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