The party, in charge of the leadership contest to replace Theresa May as Conservative Party leader and Prime Minister, did not indicate the timeframe for when the new Tory leader would take charge at 10 Downing Street after a formal handover of power.
"The announcement of the next leader of the Conservative Party will be made on Tuesday 23 July. This process has been agreed with both candidates," the Conservative Party said in a brief statement.
The two candidates were chosen from a field of 10 by the Conservative party's 313 MPs.
Postal ballots are set to be issued to an estimated 166,000 Tory party members across the UK between July 6 and 8, with polls set to close by 5pm on July 22 after which the counting process will begin for the result to be declared the next day.
A candidate achieving more than 50 per cent of the vote among Party members will be declared Leader of the Party.
According to reports, the new leader is unlikely to move into Downing Street right away, with a possible wait of a few days.
The UK Parliament's autumn recess is set to kick off from July 25, which could mean that the new prime minister is unlikely to face MPs in the House of Commons until early September.
"Parliament would express its will if there were any likelihood of that becoming an issue," Commons leader Mel Stride told MPs on Tuesday when asked about this expected delay.
Meanwhile, former foreign secretary Johnson, the frontrunner in the race, focussed on a series of interviews after his opponent foreign secretary Hunt accused him of cowardice by not agreeing to appear in a television debate.
"It's time this country frankly stopped being so down about its ability to get this thing done," Johnson said in one of many interviews, as he tried to shift the focus away from a few days of negative publicity around a domestic row with his girlfriend.
"For three years we've been sitting around wrapped in defeatism telling the British public that they can't do this or that. It is pathetic, it's absolutely pathetic," he said, in reference to Brexit.
Amber Rudd, the UK work and pensions secretary who is supporting Hunt in the race, said Johnson was making a mistake by shying away from the debates and demanded he "go further" in explaining his Brexit plan.
"This is an incredibly difficult situation and Boris needs to explain how he will deal with both sides of the Conservative Party that have concerns and try and break the impasse with the European Union. Enthusiasm and optimism is not sufficient," she said.
Both candidates will carry on travelling up and down the UK for scheduled hustings to try and swing enough votes in their favour.
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