The strikes by RMT, Aslef and Unite union members will start on the evenings of 26 January, 15 February and 17 February.
RMT General Secretary Mick Cash said the plans to introduce a Night Tube were "bodged".
London Underground called the unions' position "absurd".
It has offered a four-year pay deal over the issue and said it would hire part-time drivers to staff an all-night service at weekends.
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Aslef claimed earlier London Underground management had refused to meet to discuss conditions for working on the proposed Night Tube.
The union's London district organiser, Finn Brennan, said: "We genuinely regret the inconvenience that will be caused but the behaviour of London Underground's senior management team have left us with no other choice.
Steve Griffiths, LU's chief operating officer, responded: "The unions' position is absurd and detached from the real world."
He added: "The truth is that they expect our customers to pay for their excessive demands for even more money, fewer hours and a four-day week."
"No employer could allow this and strike action will change nothing. There is no more money."
The Night Tube, which was due to begin in September, will see 24-hour services on five lines on Fridays and Saturdays.
Tube drivers are also unhappy with pay and station rosters, according to BBC London transport correspondent Tom Edwards.
RMT general secretary Mick Cash said the union supported the principle of a "properly worked-out night Tube service" but said an "abject failure to work through the detail has led to a comprehensive breakdown in the negotiations".
London Mayor Boris Johnson said: "If a strike goes ahead, it will hit many London Underground workers who do not necessarily support the action, and it will cost the strikers in lost pay."
But Labour mayoral candidate Sadiq Khan said Mr Johnson was to blame, arguing: "It proves once and for all that the Tory strategy of refusing to negotiate or even meet with the unions makes strikes more likely not less."
Manuel Cortes, leader of the TSSA, which represents office and ticket staff, said the union will be consulting members over the next week to decide its next move.
London Underground staff are to stage three 24-hour strikes and other industrial action over pay and night Tubes.