Click the "Add a contact" icon, hover your mouse over "Add a Contact not in My Organization", then click Skype. Type in the Microsoft account of the Skype user you wish to add in the "IM Address" field, and click OK to add the contact.

1) Click the "Add a contact" icon.

2) Hover your mouse over "Add a Contact not in My Organization", then click Skype.

3) In the "IM Address" field, type in the Microsoft account name of the user you wish to add, and then click OK.

NOTE: You can only add a Skype contact on Skype for Business by using their Microsoft account address. A Skype username cannot be used.

Outcome

The Skype contact will now be added to your Skype for Business contacts.