Mr Johnson is expected to review part of the congestion charge
Boris Johnson has pledged to be a "mayor for all London" after attending the Sikh New Year festival, Vaisakhi, in Trafalgar Square.
He said he was going to "work to unite communities" in London which he said was "the whole world in a city".
The Sunday Telegraph reports he will introduce a raft of reforms as a "test bed" for a future Tory government.
Hackney North's Labour MP Diane Abbott said Mr Johnson was "an accident waiting to happen".
Mr Johnson's victory on Friday ended Ken Livingstone's eight years in office at City Hall. He will accept the seals of office from Mr Livingstone at 2400 BST.
The new mayor is expected to build bridges with the city's ethnic minority groups, after being accused during his election campaign of being a divisive figure who could not represent all of the metropolis.
Operation Black Vote's Simon Woolley said Mr Johnson "must now demonstrate that he understands what it means to govern a multi-cultural metropolis" and address issues of poverty.
At his first official engagement in Trafalgar Square, Mr Johnson was mobbed by journalists and passers-by as he joined in the Vaisakhi celebrations and posed for photographs in a policeman's cap.
He dismissed suggestions he would not support such festivals as "a canard floated by the outgoing mayor", saying he wanted to support events that brought people together.
"The last few days have been very, very exciting and very, very exhausting, but this is the single most wonderful job in British politics," he said.
"I am going to be a mayor for all London and work to unite communities.
"One of the wonderful things we have got in London is fantastic diversity - we have got the whole world in a city."
The mayor joined in Sikh celebrations in Trafalgar Square
Asked if it was true he had told Metropolitan Police chief Sir Ian Blair to cut crime or lose his job, Mr Johnson replied it was "extremely important that we get to grips with violent crime" as well as the "scourge of so-called minor crime and disorder" on public transport.
And he said violence among young people was the biggest problem the city faced and he hoped there would be an increase in educational and social activities to keep children off the streets.
"I am not pretending we can transform this overnight, but it is the job of the mayor to give a lead, and I won't rest till we have started to make a difference," he said.
His aides said he would use his first days as London mayor to start work on key pledges such as 440 police community support officers on the Tube and trains, weapons scanners at stations and a review of the western zone of the congestion charge.
The Sunday Telegraph said Mr Johnson would introduce a series of reforms as a "test bed" for a future Conservative government.
And it said he would order an inquiry into "bureaucratic waste" at City Hall - with an eye to cutting the media and marketing team by 20%.
Asked about Mr Johnson's victory in an interview with the BBC, Prime Minister Gordon Brown said he wished him well but said the "test" was now what Mr Johnson would do in the job.
Hackney North and Stoke Newington MP Diane Abbott, a Labour backbencher, said Tory leader David Cameron would be worried about Mr Johnson's capabilities.
She told Sky News: "Everybody in Cameron's office are crossing their fingers. Ken Livingstone knew about running a local authority - Boris knows nothing."