More than 90 union members yesterday voted in favour of the action, while 12 were opposed.
The move follows a ballot last week in which the Telegraph's National Union of Journalists chapel voted 76% in favour of strike action.
Staff at the newspaper said the strike was the result of the Telegraph's intentions to force 54 compulsory editorial staff redundancies, following the integration of its print and online editions.
A spokesman for Telegraph Media Group described the result of the vote as "surprising and disappointing".
"At this time of massive investment in the future of the Telegraph Media Group and the extensive changes occurring throughout our industry, the union's decision is surprising.
"It is worth noting that barely one in three of the union members voted in favour of a strike and that less than one in five of our total editorial staff are supporting the union's actions."
It is understood that the strike has been provoked by the Telegraph Group's refusal to adequately consult the NUJ chapel about its planned job cuts.
Assistant editor Corinna Honan was the most recent of a number of high-profile senior editors who have left the paper.
The Telegraph this week relocated to multimillion-pound headquarters in London's Victoria, and has invested in new-media training. However, the integration of its online and print editions has led to a surplus of production staff, and the proposed job cuts have been met with strong criticism from union members.
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