The decision to press ahead with a strike followed an 89 per cent vote for action on a turnout of 74 per cent of balloted members.
It passed the threshold in the Government's controversial Trade Union Act, under which ballots need a 50 per cent turnout for industrial action to go ahead.
A Royal Mail spokeswoman said: "Royal Mail is very disappointed by this announcement from the CWU. The Company is committed to further talks as a matter of urgency to reach agreement with the CWU. There are no grounds for industrial action. We want to reach agreement.
"In 2013, Royal Mail and the CWU committed to the Agenda for Growth – a legally binding agreement. This agreement contains contractual dispute resolution procedures. Both sides are required to follow them once instigated."
The CWU said its members in Parcelforce will be involved in the stoppage, which will be the first national postal strike since 2013.