Banbury's MP Victoria Prentis will help Boris Johnson to deliver on pledges he has made in his leadership campaign, she says.
And Witney MP Robert Courts said the country had been 'crying out' for optimistic leadership he felt Mr Johnson would provide to unite the country.
Mrs Prentis spoke after Mr Johnson was elected Tory leader by an overwhelming majority.
She also paid tribute to Theresa May, who will visit the Queen tomorrow to formally resign.
Mrs Prentis said she looks forward to showing Mr Johnson more of the Banbury constituency in the months ahead.
"After seven weeks of campaigning across the country, Boris Johnson has been elected as the new leader of the Conservative Party and our new Prime Minister," said Mrs Prentis.
"I would like to take this opportunity to welcome Mr Johnson to his new role and to wish him well for the months which lie ahead, as we prepare to leave the European Union.
"Tomorrow, Theresa May will head to Parliament for her final Prime Minister’s Questions, before going to Buckingham Palace and formally resigning as Prime Minister.
"I am grateful to Theresa May for her years of dedicated service to this country. She was, and I am under no doubt that she will remain, a devoted public servant who will continue to serve with dignity from the backbenches.
"Both Mr Hunt and Mr Johnson presented a positive vision for the UKs domestic agenda and I look forward to helping the new Prime Minister deliver on the commitments he made during the campaign to further improve our vital public services. In North Oxfordshire, we have many things to be proud of.
"I’m keen to show Mr Johnson more of the constituency and highlight the issues we are facing as a rapidly growing area," said Mrs Prentis.
"The next few months will be an important time as the new Government renegotiates our future relationship with the European Union. We need to unite the country and party, deliver on the referendum result and leave the EU as quickly and as orderly as possible."
Mrs Prentis's neighbouring MP, Robert Court in Witney, said: "“Congratulations to Boris on an emphatic victory and commiserations to Jeremy Hunt on a well-fought campaign.
"Our nation is crying out for optimistic leadership and I am confident that Boris' modern, outward-looking vision and One Nation policy agenda can unite our party and, ultimately, our country.”