"Once the interim period is over, we want a permanent, treaty-based arrangement between the United Kingdom and the EU which supports the closest possible relationship with the European Union, retaining close ties of security, trade and commerce".
Senior British ministers presented a united front to negotiations with the European Union on Sunday.
In their article, Fox and Hammond said: "We are also clear that during this period our borders must continue to operate smoothly; goods bought on the internet must still cross borders, businesses must still be able to supply their customers across the European Union, and our innovative, world-leading companies must be able to hire the talent they need, including from within the European Union". The UK wants to start talking about its post-Brexit relationship with the EU in order to reassure anxious businesses, citizens and investors, but the union has insisted that first exit arrangements should be determined.
Hammond and Fox are seen as the two ministers at opposite ends of the soft-hard Brexit spectrum and their joint article, which also said the transitional period would be "time-limited", was meant to quash speculation that the cabinet is divided on the issue.
The British government is fighting back against criticism that it is divided and unprepared for Brexit, announcing it will publish a set of detailed proposals on customs arrangements, the status of the Ireland-Northern Ireland border and other issues.
A source close to Mr Davis said the papers would highlight the British teams were "on the front foot" in the negotiations.
The third round of negotiations is due to start on August 28.
Prime Minister Theresa May will hope the intervention of the two ministers will cool temperatures in the Tory ranks amid divisions over Brexit and speculation of a possible leadership challenge when MPs return to Westminster in September.
Former top British diplomat Simon Fraser said last week the government needed to put forward a clearer position in order to move forward with the Brexit talks.
Free movement for Irish citizens in and out of Britain is expected to continue after Brexit, with the establishment of a Schengen-style area between Ireland and Britain created to resolve the border problem. He described the outcome of last year's referendum as an "unparalleled act of economic self-harm".
The UK formally triggered the Brexit process on March 29 and divorce negotiations officially began on June 19.
In June, the EU's Brexit negotiator Michel Barnier called for "more ambition, clarity and guarantees" around the protection of European Union citizens living in the UK.