Update #2 - Nothing in Europe at the moment.
Update - Sources and various GM chats seem to indicate that this is intended, and the service will be offered for free for the moment, most likely as a trial.
Cross-Realms Battle.net Invitation now Activated
It looks like the feature to invite your RealID friends from other realms has been activated on US realms today.
IMPORTANT - Since this isn't official yet, it could perfectly be a mistake from Blizzard. If that's the case you can fully expect it to be disabled soon. Don't get too excited.