Several people have asked me whether it's possible to add a widget area to the right hand-side of the Divi Theme header bar.
Here's the code to do so. It adds a widget area just below the Divi header navigation links (if you want to replace the Divi header navigation links with the widget area, you can hide the header links). The code below creates the widget area, moves it into place and then adjusts the margins around it to fit in well (and to look right on mobiles). It should be added inside php tags within your functions.php file. Note that editing PHP can break your site if you don't do it correctly, so be sure to back the site up before you use the code.
Once you've added the code, go the widget area of your WordPress admin and you'll see a new widget area called 'Header'. Drag widgets into it and they should show up in your Divi header.