There will be “bumpy moments” for UK businesses and travellers as they get to grips with new EU rules, says government minister Michael Gove.
He said there would be “practical and procedural changes” when the Brexit transition period ends on 31 December.
Mr Gove also urged people going to the EU to make extra checks, including looking at mobile phone roaming charges and passport expiry dates.
European ambassadors are due to discuss the post-Brexit trade deal later.
The diplomats will meet to determine how they can provisionally approve the deal, which was agreed on Christmas Eve, in time for the end of the transition period.
In the UK, MPs will vote on the deal on Wednesday.
Meanwhile, UK International Trade Secretary Liz Truss said she expects to sign a continuity trade agreement with Turkey this week – a move that was not possible until the deal with the EU was struck.
Mr Gove told BBC Breakfast: “I’m sure there will be bumpy moments but we are there in order to try to do everything we can to smooth the path.”
He warned businesses that time was “very short” to make the final preparations before the transition period ends.
“The nature of our new relationship with the EU – outside the Single Market and Customs Union – means that there are practical and procedural changes that businesses and citizens need to get ready for,” he said.
“We know that there will be some disruption as we adjust to new ways of doing business with the EU, so it is vital that we all take the necessary action now.”
Businesses have been urged to make sure they understand the new rules on importing and exporting goods, including the different rules that apply to trade with Northern Ireland, and to consider how they will make customs declarations on EU trade.
Mr Gove also encouraged travellers to EU destinations from 1 January to take out comprehensive travel insurance, check their mobile phone provider’s roaming charges and make sure they have at least six months left on their passports.
What happens next with Brexit?
The trade deal was reached after months of fraught talks on issues including fishing rights and business rules.
Prime Minister Boris Johnson has said it will provide new legislative and regulatory freedoms to “deliver for people who felt left behind”.
But fishermen’s leaders have accused him of “caving in” and sacrificing their interests to reach the agreement. And Labour called it a “thin deal” that needed “more work” to protect UK jobs.
Conservative grandee Lord Heseltine has urged MPs and peers to abstain when voting on the deal, warning it will inflict “lasting damage” on the UK.
The former deputy prime minister said he would “in no way share the endorsement of the legislation”, but that he would not vote against it because the consequences of a no-deal would be even graver.
Over the weekend, Chancellor Rishi Sunak sought to reassure the City of London that it will not be damaged by the deal.
He said they would be “doing a few things a bit differently” and looking at “how we make the City of London the most attractive place to list new companies anywhere in the world”.
The chancellor said the deal was “an enormously unifying moment for our country” and it brought reassurance to those who were concerned about the impact on businesses.