Johnson also urged Brexit backers to "build bridges" with those who voted for Britain to stay in the European Union after Thursday's bitterly divisive referendum and played down the prospects of Scottish independence.
Johnson - who visited Boston a year ago during the Hub's ill-fated pursuit of an Olympic bid - emerged as a leading contender for the country's top position after he aligned himself with leaders of the so-called "Leave" camp, who pushed for the successful vote to break from the EU.
Mr Johnson was pictured welcoming Remain campaigners Jake Berry, Amanda Milling and Ben Wallace, alongside Leave's Nigel Adams to his Oxfordshire home on Sunday.
The Conservative MP and high profile Leave supporter left his London home without giving any reaction to the UK's decision to vote to leave the EU.
Jeremy Hunt, who announced his intention to run for leader, received one per cent.
Mr Johnson is seen by many as the frontrunner to replace his schoolmate and once close friend Mr Cameron, who announced he would resign in October after the British public voted in favour of Brexit.
Known for his unconventional political style, the 52-year- old journalist-turned-Conservative politician Johnson had led the Brexit camp in the June 23 referendum, falling out with his mentor and party leader Cameron who aggressively campaigned for Britain to stay in the 28-member EU.
Johnson yesterday insisted the United Kingdom will always be part of Europe and enjoy "intensifying" co-operation with other nations, as he set out his vision of post-Brexit Britain.
George Osborne, once touted to be David Cameron's successor, may work alongside Johnson and Gove after he made peace in a text message following the vote result.
"In the end this question is about the people, it's about the right of the people in this country to settle their own destiny", he said. Both have a mutual loathing for Mr Johnson, though, and will want to prevent him from taking the top job.
Yesterday Nick Boles, the business minister, became the first senior Cameron ally formally to endorse Mr Johnson's bid.
"I would like to see them unite and bring our party together without the need for a leadership contest if we can possibly manage that".
That was before the two Conservative Party members found themselves on opposite sides of the referendum.
"The British people have voted to leave the European Union and their will must be respected", Cameron said in a press conference Friday morning.