Custom Styles in SharePoint Rich Text Editor

All you need to do is to add the class names in the style sheet 

Format specified below

.ms-rteCustom-<Name of the class>

If you are using custom css file then just add the styles in the end of the css file and add the reference in your master page.

If you are not using any custom css file then you can either change the core css file if you need to make this change across your farm else just create a custom css file and upload in the style library and then got to master page settings and override css file link there.

Now these styles appear in Rich Text editor as well as in content web part and content editor web part.

Example 

.ms-rteCustom-ForeColorGreen{Color: Green;}