Britain is currently represented in the 164-member body through its membership of the European Union, but when it leaves the bloc it will need to establish its own terms, or schedules.
"In order to minimise disruption to global trade as we leave the EU, over the coming period the government will prepare the necessary draft schedules which replicate as far as possible our current obligations," Fox said in a written statement to parliament.
"This work is a necessary part of our leaving the EU. It does not prejudge the outcome of the eventual UK-EU trading arrangements."
Prime Minister Theresa May has promised to begin formal exit talks with EU leaders by the end of March, but has refused to give a "running commentary" on her negotiating strategy.
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She says she wants "maximum possible access" to the European single market after Brexit, and last week a senior minister, David Davis, suggested the government would consider paying for this.
May has also stressed she wants to control immigration, putting her at odds with EU leaders who say freedom of movement is a pre-requisite of membership to the single market.
"We have the diplomatic experience and economic gravity to be a considerable ally to those countries who share our values on free trade, and our vision for the global economy.
"Director General (Roberto) Azevedo has already offered his support and that of the WTO Secretariat as we consider our transition to becoming an independent member.