How do you appear offline to friends on Battle.net?

The option to appear invisible was anounced back in 2012 but was missing from Battle.net for a long time and a 2014 tweet mentioned that it wouldn't be included for some time.

New Update: It's Here:
As of October 2017 the option to appear offline is implemented in the beta version of the Blizzard Battle.net app and will come to the standard version later. (There are also other new features like groups and chat channels coming to the app.) See this announcement from Blizzard for more details.

(See the previous revision of this answer for some now outdated information.)

Currently (as unfortunate as this is), there is no option to appear offline to friends which are added to the battlenet list. The only option is to remove them and add them on again later, but this does not really do the job as other networks like skype or the like do it.