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 mobile phone roaming charges.
EU ambassadors have approved the post-Brexit trade deal, paving the way for it to take effect on 1 January.
Under EU rules it can take effect provisionally, though the European Parliament will vote on it in January.
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.