The unit - reportedly dubbed ‘Taskforce Europe’ - will replace the Department for Exiting the European Union when it shuts down on 31 January, the date on which Britain is due to leave the EU.
According to both The Sunday Telegraph and The Mail on Sunday, the team will be run from the heart of government in Number 10 and the Cabinet Office, with personal oversight from the Prime Minister.
It will be led by Mr Johnson’s most senior Europe adviser David Frost and will be responsible for implementing the Withdrawal Agreement as well as leading on negotiations for a free-trade agreement with the EU.
The naming of the group mirrors that of the EU side, which has set up its own ‘Task Force for Relations with the United Kingdom’.
A Government source said: "In 2020, we will move forward to establish a future relationship and free-trade agreement with the EU.
"Following the election, the Government has a clear and renewed mandate to achieve this. We want our new relationship to be based on an ambitious free-trade agreement, and a close friendship between sovereign equals."
The reports of a new unit to lead on a post-Brexit deal with the EU come after the president of the European Commission cast doubt on Mr Johnson's timetable for agreeing a pact.
Britain is currently due to remain in a transition period with the EU, staying broadly aligned with its rules, until the end of 2020.
But Mr Johnson has vowed not to extend that period, fixing a deadline to discussions on the deal that will replace it.
Ursula von der Leyen, who took over from Jean-Claude Juncker earlier this month, said she had “serious concern” over the limited time available for the second round of talks.
She told French newspaper Les Echos: "It’s not only about negotiating a free trade deal but many other subjects."
And the Commission president added: "It seems to me that on both sides we must ask ourselves seriously if all these negotiations are feasible in such a short time."
But government sources told the Mail on Sunday that Ms von der Leyen's comments were "tactics and bluster" and argued that any "genuinely held concerns about timing" should have been raised during talks on the Withdrawal Agreement.
