Britain is set to officially leave the EU in March 2019, but plans to abide by many of the EU's rules for around two years to make the transition more orderly.
Davis said that Britain and the EU should have agreed the "substantive" terms of their permanent future relationship by March 2019.
But the structure of the transition deal, which is expected to run until 2020/21, is the cause of heated debate.
"I'm relaxed about transition because my primary concern is about the future relationship, that's what matters, that's what people will judge us on in 10, 20, 30 years time."
The minister said a transition deal was essential to give governments and businesses time to adapt to the future arrangement.
Davis said that during this period, "we will be replicating to a very large extent the operations of the single market and customs union" and that Britain would remain subject to the European Court of Justice (ECJ).
"If on 30 March 2019, the UK is subject to the ECJ, takes new rules relating to the single market and is paying into the European budget, are we not a vassal state?" asked MP Jacob Rees-Mogg.
Davis replied that in the future Britain would no longer be bound by the rules of membership of the EU's custom union that are currently preventing it from negotiating trade deals with nations outside the EU.
However, he did admit that this issue could be a sticking point in upcoming negotiations on the transition deal and that Britain would probably have to abide by new rules handed down by the EU during the transition, without having a say on them.
Davis moved to calm fears of EU citizens living in Britain, saying they would be taken care of even if Britain crashed out without a deal.
"One way or another we will resolve this issue. I'd say to anyone who is worried about this issue: don't be," he said, calling it a "moral issue".
Representatives from Britain's Brexit department have been meeting with EU officials in Brussels in recent weeks, said Davis, but formal negotiations will restart in March.
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