The Transport Salaried Staffs' Association will walk out with Aslef, RMT and Unite on 5 August in a row over servicing the new Night Tube service.
London Underground said it had made a "fair" offer and would continue to be available for talks.
The four unions previously walked out on 9 July causing the entire Tube network to shut down.
Talks had been held at conciliatory service Acas on Tuesday.
But TSSA's general secretary Manuel Cortes said: "We were expecting to agree a framework to discuss all our concerns over staffing levels and safety at the Night Tube as well as the pay issues.
"But all we got was a repeat of the 'take or leave' final pay offer which has already been rejected and no detailed talks on the Night Tube. We are willing to negotiate, they clearly are not."
Steve Griffiths, London Underground's Chief Operating Officer, said: "We have made a very fair and reasonable offer on pay and the introduction of the Night Tube and we continue to urge the trade unions to put it to their members.
"We will be at ACAS this week for further discussions to resolve this issue and trust the trade unions will be too."
The row is over a 2% average pay rise offer for LU members and workers' terms and conditions linked to plans to introduce an all-night Tube service on the Jubilee and Victoria lines and and most of the Central, Northern and Piccadilly lines.
Last week's strike saw long delays and rush hour began earlier than normal as commuters tried to find alternative ways to get to and from work.
A fourth union has announced it will be take part in a 24-hour Tube strike next month in a row over pay and conditions.