In a brief speech to supporters at City Hall, Mr Johnson quipped that he was certain there were "shredding machines quietly puffing and panting away" throughout the building as his Labour predecessor prepared to move out.
Mr Johnson officially takes over as mayor at midnight on Sunday but began his policing and transport briefings immediately after signing the declaration of office.
Both Metropolitan Police Commissioner Sir Ian Blair and transport commissioner Peter Hendy were on hand for Mr Johnson's inaugural speech.
Elected on what he described as "a very, very clear series of manifestos", Mr Johnson said he would waste no time in implementing his wide-ranging agenda.
Key priorities include making public transport safer.
Mr Johnson spoke about crime hours after a boy was killed in London
"We are going to double the size of the safer transport teams to get people the sense of safety and security on the buses that they deserve," he said.
"I think there is a vital necessity to drive out so-called minor crime and disorder as a way of driving out more serious crime."
Just hours after yet another teenager was stabbed to death in the city - the twelfth teenager killed this year - he said he would use the resources of the mayor's office to address youth violence.
"This problem of kids growing up without boundaries and getting lost in tragic and self-destructive choices is the number one issue we face in this city.
"It is the job of me as mayor to lead the fight back against it and that is what I want to do and I hope you will all join me in doing it."
Other items on his agenda include revisiting the controversial congestion charging policies in central and west London, building 50,000 more homes, increasing river transport options and amending the London Plan to ensure back garden space is protected from development.
Mr Johnson said his new job included the need to build bridges with communities.
"It is vital for a mayor of London to bring people together, and to unite London, and to serve every community in London impartially."
In his earlier victory speech, Mr Johnson praised Mr Livingstone for his public service.
"You shaped the office of mayor. You gave it national prominence and when London was attacked on 7 July 2005 you spoke for London."
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