The Chancellor Philip Hammond and the International Trade Secretary, Liam Fox, write that the transition period is created to avoid a so-called "cliff-edge" - but their comments in the Sunday Telegraph don't reveal how long this period will last.
Their comments are being seen as an attempt to show unity between rival sides in Prime Minister Theresa May's Cabinet.
"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", they said.
The two leading politicians said the government wanted to ensure "there will not be a cliff-edge when we leave the EU".
The government says it hopes to persuade the 27 other European Union nations to start negotiating a "deep and special" future relationship that would include a free trade deal between Britain and the EU.
Writing in a joint article in the Sunday Telegraph, two of Prime Minister Theresa May's most senior ministers said that the United Kingdom will seek a transition deal for leaving the European Union, but that any deal will not be a "back door" to staying in the bloc and would be limited in its time period.
They wrote in The Sunday Telegraph: "We want our economy to remain strong and vibrant through this period of change".
Over the coming 10 days, a number of Government papers will be published spelling out the UK's Brexit blueprint on key issues including the customs union, the Irish border, fisheries and agriculture.
The British government has said it will give more details about its policies on Brexit next week.
Some still dispute her approach, with former foreign minister for the now-opposition Labour party David Miliband and pro-EU Conservative MP Anna Soubry warning in Sunday newspapers of the economic "self-harm" of leaving the single market.
Mr Miliband, who narrowly lost out to his brother Ed in the 2010 Labour leadership contest and who now heads the International Rescue Committee relief agency in NY, described the outcome of the 2016 referendum as an "unparalleled act of economic self-harm". We should. But democracy did not end on June 23 past year.
"The referendum will be no excuse if the country is driven off a cliff", he declared.
Britain's Brexit Secretary David Davis is due to hold a third round of talks with the EU's chief negotiator Michel Barnier in Brussels at the end of August.
This is published unedited from the PTI feed.