1 July 2016 Last updated at 11:22 BST
The Leave campaigner, who shocked Westminster on Thursday by pulling out of the Tory leadership race, said: "It's going to be up to someone else now."
Asked what he thought of his fellow Leave campaigner Michael Gove's decision to run instead, Mr Johnson added: "I wish him every possible success."

In July, Conor McGinn, who is from south Armagh, claimed the Labour leader suggested phoning his father.
It followed an interview in which he called for Mr Corbyn to "reach out beyond his comfort zone".
A spokesman for Mr Corbyn said at the time that it was "untrue".
The St Helens MP told BBC Radio Four's Westminster Hour: "The modus operandi that he (Mr Corbyn) and the people around him were trying to do, involving my family, was to isolate and ostracise me from them and from the community I am very proud to come from -  which is an Irish, nationalist community in south Armagh."
The MP claimed that after he spoke out about Mr Corbyn in May, he got a call from the Labour whips' office saying the party leader had initially asked for his resignation and then considered sacking him.
But subsequently, through his spokesman, he had asked for an apology and retraction, which Mr McGinn refused to make.
The MP said he then texted the Labour leader to make clear no offence was intended and reiterate that their friendship was important to him and asking for a meeting.
He received no response, but said he was then informed by the whips' office that Mr Corbyn had proposed asking the MP's father, Pat, to intervene.
Pat McGinn was Sinn Féin councillor in Newry for many years, serving as the council's mayor between 2005 and 2006.

The arrests are part of an operation that has seen women targeted for posting photos showing them not wearing headscarves on Instagram and elsewhere.
Women in Iran have been required to cover their hair in public since 1979.
The eight unnamed people were among 170 identified by investigators as being involved in modelling online.
They included 59 photographers and make-up artists, 58 models and 51 fashion salon managers and designers, according to a statement from the court.
The arrests were announced by the court's prosecutor Javad Babaei during a state television programme broadcast late on Sunday that focused on the "threats to morality and the foundation of family" posed by social media.
Mr Babaei claimed modelling agencies accounted for about 20% of posts on Instagram from Iran and that they had been "making and spreading immoral and un-Islamic culture and promiscuity".
Of the 170 people found to be involved in online modelling, 29 were warned that they were subject to criminal investigation, the prosecutor added.
"The persons who reformed their behaviour after receiving a notice did not face any judicial action, and eight out of the 29 have been arrested," he said.
A spokesman of the Iranian Centre for Surveying and Combating Organised Cyber Crimes, Mostafa Alizadeh, said: "Sterilising popular cyberspaces is on our agenda.
"We carried out this plan in 2013 with Facebook, and now Instagram is the focus," he added, saying fresh operations would begin in the coming days.
There was no immediate comment from the photo-sharing site Instagram, which is owned by Facebook.

The Canadian, 28, was picked as the Devils' forward of the year in 2016-17 after scoring 24 goals and 29 assists in 66 games.
Haddad was a dominant force last season, playing the role of a power forward as Devils won the Elite League.
"Joey Haddad was outstanding for us last season," said Devils player-coach Andrew Lord.
"There were a number of games that he completely took over or broke open a game for us and that is what makes fans love him so much.
"He is a big body and dominates in the corners and is tough to play against.
"There were a number of teams that wanted him to make a move but he loves it here and I don't really think he entertained any other offers."
Haddad will also be a vital part of Devils' Champions Hockey League campaign, with the Welsh side drawn in Group E against HC Davos from Switzerland, Bili Tygri Liberec of the Czech Republic and Sweden's Vaxjo Lakers.
Boris Johnson has been quizzed by reporters as he left his home in London this morning.
[NEXT_CONCEPT]
A Labour MP who accused Jeremy Corbyn of threatening to use his father - former Sinn Féin mayor Pat McGinn - to "bully me into submission" has spoken publicly about the row.
[NEXT_CONCEPT]
Iran has arrested eight people working for online modelling agencies deemed to be "un-Islamic", the prosecutor of Tehran's cybercrimes court has said.
[NEXT_CONCEPT]
Cardiff Devils attacker Joey Haddad has re-signed for a fourth season with the Elite League champions.