Video report by ITV News Political Correspondent Angus Walker
The 109 new MPs will join remaining Tories in voting on the PM's deal this Friday as the Government begins its push to take Britain out of the European Union next month.
He said the MPs must "repay the trust of the electorate" by working "flat out" on achieving Brexit and voting for his deal, which he told them will return to the Commons "now".
He told the group of new MPs they have "not only changed the political map of this country, you've changed our party for the better."
He added: "What we're going to do now is work with you to change our whole country."
The Withdrawal Agreement Bill (WAB) will be brought before the Commons on Friday – and could be debated at first and second reading in one day, if the Speaker agrees to the timetable.
Upon meeting her new boss, Flick Drummond, the new MP for Meon Valley, said the PM was "very inspiring".
"He talked about how excited he was to see so many of us here. He said we are here to get things done. We are here to get Brexit done," she said.
Caroline Ansell, MP for Eastbourne, said: "There is a real energy, a real buzz. Everybody is very keen to move forward."
Paul Howell, who took Tony Blair's old Sedgefield seat, said: "It is a fabulous occasion. It is a new profile for the Conservative Party. We have got to deliver across the country."
ITV News Political editor with the latest on Boris Johnson's plans
The Prime Minister’s official spokesman told a Westminster briefing: “We plan to start the process before Christmas and will do so in the proper constitutional way in discussion with the Speaker.”
Asked if the legislation would be identical to that introduced in the last parliament, the PM’s spokesman said: “You will have to wait for it to be published but it will reflect the agreement that we made with the EU on our withdrawal.”
The Government would attempt to push the WAB through its final Commons stages in January, and will hope the Bill then clears the Lords quickly to allow the UK to leave the EU on January 31.
However, approving the legislation will not mean the Brexit saga is over. The UK will remain in the EU until at least the end of 2020 during the implementation period.
This time will be used by Brussels and London to hammer out a trade deal and decide on their future relationship on subjects such as security.
But EU figures have been highly sceptical this can be sorted within the year, with chief negotiator Michel Barnier saying the timetable was “unrealistic” in leaked comments.
Senior Cabinet member Michael Gove, who is the Chancellor of the Duchy of Lancaster, tried to dismiss these fears.
He told Sky's Sophy Ridge on Sunday he is "confident" the agreement could be finalised by the deadline because "quite a lot of the details" are agreed in the Political Declaration agreed with the EU.
Mr Johnson is not the only leader who will be welcoming a new intake of MPs on Monday, with the SNP's Westminster leader Ian Blackford expected to meet his new colleagues.
Mr Johnson will undertake a minor Government reshuffle later on Monday to fill gaps left by departures before making more radical changes in February.
The posts of Culture Secretary, Welsh Secretary and Environment Minister are expected to be filled.
The Queen will formally open Parliament on Thursday when she sets out the Government’s legislative programme during a slimmed-down State Opening.