The strike will include civil servants from UK government departments and agencies, as well as the Welsh Government, but will exclude Scottish Government bodies.
The Public and Commercial Services (PCS) union, which has 270,000 members and is the largest civil service union, said the day will form one element of a 72-hour strike also involving unions in the health service on 13 October, and local government on 14 October.
The focus of the strikes will be pay: wages were frozen for two years after 2010, and pay rises have since been capped at 1%. The PCS believes that given pay constraint, pension changes and inflation, many civil servants have suffered a 20% cut in their real incomes under the coalition.
PCS general secretary Mark Serwotka said: "These strikes show we are serious about bringing an end to pay cuts that have slashed the living standards of public servants while the super-rich have been rewarded with tax cuts.
"Until we chase down the tax dodgers and invest properly in our communities and public services, the so-called economic recovery will only ever benefit millionaires, while the millions pay the price."
The planned action follows a joint public sector strike on 10 July, when PCS members marched alongside representatives from unions including the National Teachers Union, GMB and Unison.
A Cabinet Office spokesperson said: “It is disappointing that, once again, some union leaders insist on strike action that benefits no one.
"As part of its long-term economic plan, this Government has taken tough decisions to address the budget deficit, including freezing public sector pay for two years, while protecting the lowest paid.
"Pay restraint protects jobs, supports high-quality public services and helps get the UK’s finances back on track.
“PCS continues to rely on a mandate for action that is over a year old, and the results of a ballot supported by less than a fifth of its members. Without a proper new mandate, this strike action lacks authority.”