I recently ran into an issue of needing to redirect visitors to a WordPress site from one server (foobar.com) to another (roofab.com). The content was staying exactly the same, so the redirect just needed to swap the domain name of the first site for the domain of the second.
You can do this with the .htaccess file if your host allows that but, if you don’t have that access, I found a really easy plug-in that you can add to the first WordPress site. Taylor Lovett’s Safe Redirect Manager can handle multiple redirect rules, if you need them, and applies the appropriate status code so that search engines like Google know it is a legitimate redirect.
In my case, I used the * wildcard to redirect all content but you could do just certain content. The destination was the new domain (roofab.com) with the same wildcard. It will also redirect your RSS feed, so people who are following your feed will continue to get it, giving you a chance to warn them about the change. It does not forward your wp-admin area, so you can always get back and disable the plugin from the dashboard if you have to.
This was almost too easy. If you find dithering about with .htaccess files a pain or beyond your skill level, this is a great alternative.