Search and replace for posts and pages

I’m about to migrate a site to a new web address.

Within a number of posts and pages there are links that point to what will become the old site address.

Is there a plugin that will go through my posts and replace the old address with the new address?

I’ve got a plugin that will do this for the database, but I don’t think it does that for links coded into the posts and pages.

Most of the plugins I have seen seem to do this one the fly each time the page is loaded, but I want a plugin that will physically change the page content in a one time event.

Any ideas?