So this is what worked for me:
Click on the Project name in "Project navigator"
Click on the "Info" tab
Unfold "Custom iOS Target Properties" section (should first one)
Add there "Fonts provided by application" key, however not at the bottom somewhere in the middle.
Now you can close this window and open it again and see the "Fonts provided by application" key somewhere in the middle.
Populate items of this key with names of your custom fonts.