The government has pledged an extra £236m to tackle rough sleeping, alongside an urgent review into the issue by a former homelessness tsar.
The new funding will go towards accommodation for up to 6,000 rough sleepers, and helping those at immediate risk of being on the streets.
Labour said the government was "in denial about the scale" of the problem.
But Boris Johnson said he was "absolutely determined to end rough sleeping once and for all".
The announcement comes ahead of new homelessness figures, set to be published on Thursday.
On Wednesday, the BBC revealed more than 28,000 people in the UK were recorded sleeping rough in 12 months, with five times as many rough sleepers in England than the government's published statistics.
The government said it had already committed £437m to tackle homelessness and rough sleeping in 2020/21, but No 10 said the £236m was additional money to help it meet its manifesto pledge to end homelessness within the parliamentary term.
The funding will be used to buy new accommodation, refurbish existing units, and to lease private rented sector properties for those already rough sleeping or those at risk.
"It is simply unacceptable that we still have so many people sleeping on the streets," said Mr Johnson
"We must tackle the scourge of rough sleeping urgently, and I will not stop until the thousands of people in this situation are helped off the streets and their lives have been rebuilt."
Dame Louise Casey will lead the review into the issue to provide advice to both the PM and Housing Secretary Robert Jenrick on what other action should be taken.
Her work will look into the link between 24-hour street activity and rough sleeping, as well as look into the effects on people struggling with drug and alcohol misuse, and with physical and mental health issues.
Dame Louise said: "Homelessness, and within that rough sleeping, is something that's causes misery, so I hope that I will be able to help the government and the country expedite action on this issue."
A new minister dedicated to rough sleeping has also been confirmed as Adam Holloway, who will serve as Mr Jenrick's parliamentary private secretary in his department.
'Ten years of failure'
Labour's shadow housing secretary, John Healey, said the BBC's research showed the government was not doing enough.
"The Conservatives are in denial about the scale of street homelessness, with new figures showing that the government's own statistics are seriously misleading the public about the number of people sleeping rough.
"After 10 years of failure, the Conservatives should adopt Labour's plan to end rough sleeping for good."
The chief executive of homelessness charity Shelter, Polly Neate, said said it was right for the PM to take on the problem, but said there was "no great secret about what is causing this emergency".
"As we see in our services day in and day out, most people are tipped into homelessness simply because there are not enough affordable, safe, and secure homes in this country," she said.
"The bottom line is people can't afford to live anywhere - a problem made infinitely worse by a dire lack of social homes and cuts to housing benefit."
Ms Neate added: "Emergency measures to get people off the streets quickly and housing first pilots can only go so far, if you don't have the stable homes to back them up."