City authorities hope to expand homeless shelters and build quality housing over the next 10 years.
It is "the most serious humanitarian crisis confronting our county today," city official Sachi Hamai said.
LA declared a state of public emergency last year as the number of homeless people soared by 12.4% in two years.
Residents and officials say a mixture of unemployment, drugs and rising rents and house prices are to blame for the growing problem.
As many as 40,000 homeless people are predicted to be living in the whole of Los Angeles county, two-thirds of which either live in the street, in tents or in cars.
Measures to be introduced as part of a 10-year-plan include investing in short and long-term housing, allowing overnight parking for people living inside their vehicles, and creating a city-wide network of mobile showers and toilets.
Officials are to release $150m over the next two years, which will be earmarked for housing the homeless. Some lawmakers are questioning the source of the funds, but the city's mayor has indicated that it could come from new revenue and by shifting existing funds.
"It may include things that have to do with revenue growth or the shifting of priorities of money. We don't have 100 million extra dollars lying around where we can go, 'OK we were going to split this up into other things, let's just put it all into homelessness.' It will require difficult decisions," Mayor Eric Garcetti said.
The plans still need to be adopted by the city, which will not be voting on its budget until April.
Los Angeles already spends some $1bn a year on medical, psychiatric and social welfare costs on its homeless residents.
The City of Angels has another nickname: the homeless capital of America.
The accuracy of the title may be disputed - there are many ways to count, none of them definitive - but no one else wants it, and it has stuck.
The heart of this capital is in the shadows, beneath the gleaming skyscrapers, on Skid Row in downtown Los Angeles.
In this land of glitz and glamour, the forgotten people have made camp.
Block after block, the homeless and their scant belongings - tarpaulins, tents and trolleys - are scattered on the concrete in the baking sun. Most of the faces are African-American.
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Los Angeles, known as the homeless capital of the US, has passed a $1.87bn (£1.29bn) plan to help get an estimated 40,000 people off the streets.