The UK will be out of the EU customs union and single market by March 2019, David Davis said.
The Brexit Secretary said he expected the UK to have left the arrangements within the two-year timetable set out under the Article 50 process.
His comments came as Chancellor Philip Hammond repeated his call for a transitional deal to avoid a "disruptive and dangerous cliff edge" in trading links with the European Union after Brexit.
But Downing Street sought to shut down public discussion by ministers about the length of any transition or implementation phase, insisting that this will be part of the Brexit negotiations.
A Number 10 spokeswoman said: "The position the Prime Minister has set out many times hasn't changed. It's not in anyone's interest for there to be a cliff-edge. We want to give certainty to businesses.That's the position of David Davis and Philip Hammond also.
"What the Prime Minister has been clear about is that clearly leaving the EU means we will be leaving the Customs Union. What that looks like and the phases of implementation and so on will all be subject to negotiation."
Addressing company executives at an event hosted by The Times, the Brexit Secretary said he believed exit talks would be done by the two-year deadline.
Asked if the UK would be straight out of the customs union, he replied: "I would have thought so."
The Brexit Secretary said any transition period was likely to end in 2022 as he described Mr Hammond's previous comments on the potential timescale as "not quite consistent with one another".
He added: "What he's actually said, the most important thing is it's got to be done before the election so that's a maximum of three years."
Mr Davis said he was "entirely aligned" with the Chancellor on putting jobs and prosperity first.
"I firmly believe that our approach puts jobs and prosperity first. So much so I didn't even think it was necessary to say it at the beginning," he told The Times CEO Summit.
Mr Davis said there would be "practically no burden" on businesses at all under the Government's plan to extend rights to EU citizens already living in the UK.
He added: "My job is to bring back control of migration to Westminster. It is not to slam the door on immigration.
"We will bring immigration down, but in a way and at a pace that does not cause labour shortages, or worse, undermine the nation's need for new talent."
Mr Hammond, speaking in Berlin to the CDU Economic Council, insisted there had to be a "smooth and orderly path" to the new arrangements under any Brexit deal.
Although he did not put a timescale on the transitional process, Mr Hammond said: "Whether it is the British importer renewing a contract with a French component supplier, the German car exporter investing in its UK distribution network, the Dutch grower who is making a contract with a British supermarket chain or the Italian electricity company hedging its exposures through London's financial markets, they all need certainty, well ahead of time, that they won't have tariffs suddenly imposed on them part-way through their contracts, or that their shipments won't face customs delays and bureaucratic costs, or that the enforceability of their contracts will not be called into question.
"Early agreement on these transitional arrangements, so that trade between our countries can carry on flowing smoothly, will reduce uncertainty, unlock investment decisions, instil business confidence and protect jobs and prosperity, in Britain, in Germany and across this continent."
In a side-swipe at Foreign Secretary Boris Johnson's position of being in favour of "having our cake and eating it" by securing all the benefits of EU membership without the drawbacks, Mr Hammond said: "The question is not whether to have cake, or eat it or even who has the largest slice, the question that matters is whether we can be smart enough to work out how to continue collaborating together, to keep the cake expanding, for the benefit of all."
Roland Rudd, chairman of Open Britain - which is campaigning against a hard Brexit, said: "To protect our economy during the Brexit process, it is vital that the Government negotiates a transitional period that keeps Britain in the single market and customs union until a trade deal that gives us the 'exact same benefits' can be negotiated.
"It is truly concerning that the Brexit Secretary appears to have ruled this out.
"I hope that common sense wins the day within Whitehall, and the Chancellor and other ministers make their views known and prevent a hard Brexit with no transition that would put our economy at risk."