Redirect All Pages To New Directory/Location Automatically

For years, I’ve had my WP installed at http://www.mydomain.com/blogs but I now want to eliminate the /blogs and redirect visitors to the new URL automatically anytime they try to get to the old one. I know how to change the WP URL in Settings and point the domain to the new directory, but am having difficulty with automatically redirecting the old links.

For instance, if they try to go to http://www.mydomain.com/blogs/story I want them automatically redirected to http://www.mydomain.com/story. I’ve found various methods of modifying the .htaccess but they all just redirect each old page to the root of the site instead of its equivalent new page URL. I know I could do it each one individually, but what a pain.

Also, the site used to have a different domain years back, I’d like to redirect everyone from http://www.olddomain.com/story to http://www.newdomain.com/story automatically. I have been able to set it up where either URL works when used, but I can’t figure out how to automatically redirect users.

I tried doing this in my cPanel, but it gives me an error saying I’m creating a redirection loop.