The Brexit Secretary expects an implementation period to be agreed in the first quarter of next year, and a trade deal by 2019.
David Davis has urged EU member states to ignore claims by the bloc's chief negotiator a post-Brexit trade deal could take "several years" to complete.
The Brexit Secretary dismissed the stance of Michel Barnier, who has suggested an EU-UK trade agreement will only be reached a while after Britain's formal departure in March 2019.
Mr Davis also told MPs he expects the outline of a transitional period, which could last around two years, to be agreed within the first three months of next year, making it "pretty plain what we're trying to deliver".
Appearing before the House of Commons' Exiting the EU committee, Mr Davis claimed countries such as Belgium, France, Holland and Denmark would lead calls for the EU to agree the terms of Britain's future relationship in the next 18 months.
EU leaders have agreed to begin internal preparatory discussions on the next phase of Brexit negotiations, on future trade and a transitional period, and could authorise the start of those talks at a European Council summit in December.
Mr Davis suggested some EU member states had "really serious investment" in the UK, with the absence of a Brexit trade deal set to impact their economies by 3-4%.
Mr Davis expressed his hope EU leaders would use their December gathering to decide their guidelines for the second phase of Brexit talks, but admitted it is "unlikely" they will agree the framework for a transitional period then.
His words offered a clarification of the Prime Minister's apparent suggestion earlier this week that a transition deal could only be agreed once the terms of Britain's future relationship are known.
On a Brexit trade deal with the EU, Mr Davis added: "That won't be agreed in detail until 2019."
He suggested it could also be subject to mild alterations after 2019, as EU member states ratify the agreement.
The Secretary of State also raised the prospect of Parliament only having a vote on the final Brexit deal after Britain formally leaves the bloc.
Mr Davis claimed a Brexit trade deal and the UK's withdrawal agreement might only be agreed concurrently as late as March 2019.
Mr Davis also rejected Mr Barnier's claim the UK is set for a Brexit trade deal similar to Canada's agreement with the bloc, after Theresa May chose to leave the EU's single market and customs union.
He said: "The Prime Minister has made plain we are looking for a bespoke agreement."