LiteSpeed Cache

If your host offers Litespeed Cache for WordPress, you can use the Litespeed Cache plugin to accelerate your website.  One of the Beta features of this is WebP image replacement.

Pros

This plugin can save you tons of bandwidth for big images if your site already has them in the library.  This plugin will also help you score higher on Pingdom, GTMetrix, Pagespeed and friends.

Cons

This has a caveat.  This replaces images in groups, so it generates optimized files per image submitted as well as a backup of the original image.  As a result, you’ll need to closely monitor disk and inode usage if your image count is in the thousands.  Usage of WebP images result in faster load times, and are highly compressed so not as much bandwidth is needed to download the image.  The resulting optimized image filesize is most often smaller.

You can accomplish this task by yourself, however the plugin handles most everything.