WordPress permalinks vs "dot.php"

I am in the process of completely re-doing a non-Wordpress site and making it WordPress.

With my non-Wordpress site the pages end with .php.
With WordPress they end with the name of the page or post but no extension.

So, there is no way to replace a page called http://www.mysite.com/links.php with the same url in WordPress because in WordPress it would be http://www.mysite.com/links/?

This would mean that an old page with the .php extension that currently is recognized by search engines, once all the information from that page is transferred to a WordPress page, the search engines would have to start from scratch and search engine status would be completely lost initially?

Is there any way around this?