The council backed a French-drafted resolution to send up to 228 police for an initial period of a year.
Burundi earlier said it would accept no more than 50 police officers.
More than 400 people have been killed in unrest since President Pierre Nkurunziza said he would run for a third term in office last April.
More than 200,000 people have fled their homes.
"Given an increase in violence and tension the Security Council must have eyes and ears on the ground to predict and ensure that the worst does not occur in Burundi," said French UN Ambassador Francois Delattre.
"This is a strong act of preventative diplomacy," he added.
The government of Burundi earlier warned it would agree to no more than 50 UN police officers.
Diplomats are now negotiating how to implement the UN Security Council's resolution.
Although both Burundi's opposition and government forces are ethnically mixed, some fear that the violence could descend into a repeat of the genocidal killings which the country has previously experienced.
President Nkurunziza is the former leader of a Hutu rebel group which battled a Tutsi-dominated army for many years until he came to power in 2005 as part of a peace deal.

Kate McCann set off from Edinburgh on Saturday morning with about 20 other cyclists.
The five-day challenge is in aid of the Missing People charity.
It will pass through Newcastle, York, Nottingham and Northampton before crossing the finish line in London on Wednesday.
Mrs McCann is an ambassador for Missing People and last year launched Child Rescue Alert, which has seen more than 250,000 people sign up to receive alerts when a child is feared to have been abducted.
Her daughter Madeleine was three when she went missing from the family's holiday apartment in Portugal's Algarve on 3 May 2007.
The case has become one of the most famous missing persons cases of all time.
Mrs McCann said: "The night that our little girl was taken from her bed, we mistakenly presumed that an alert would have gone out immediately to the public to get as many eyes and ears involved in the search as possible.
"But no such system existed to get a message out into the public domain quickly and recruit help.
"Although a simple idea, Child Rescue Alert is a potentially life-saving system, the success of which is reliant on us, as members of the public, to sign up to receive free alerts when a child goes missing.
Mrs McCann launched the child rescue alert scheme with the mother of murdered schoolgirl April Jones last year.
The scheme is designed to use social media, text messages, email and digital billboards across the UK in addition to traditional broadcast media to issue alerts.

The main feature was a drop in bank shares.
That came after the news that Deutsche Bank faces a $14bn penalty to settle an investigation by US regulators into the mis-selling of mortgage-backed securities.
Shares in RBS fell by 4.4%, Barclays by 2.8% and Standard Chartered by 2.7%.
Neil Wilson, from ETX Capital, said the Deutsche case could have serious implications for RBS which was "among a number of European institutions that could face similar claims from the US Department of Justice", he said.
"RBS could have to pay up to $13bn to settle the claims.
"Even a third of this figure could deliver a crippling blow to the lender, making its return to profitability even further off. It would also derail plans to return the bank to private ownership any time soon," Mr Wilson added.
Among the main risers in London were TUI, up nearly 4%; Shire, up 3.2%; and Burberry, up 3%.
On the currency markets, the pound fell 1.2% against the dollar to $1.309 and dropped 0.4% against the euro to â‚¬1.1730.

Most of the deaths resulted from a stampede as hundreds of students rushed to escape the blaze through two exits, the Kano state officials said.
Twenty-five others were injured in the fire which broke out as students were sleeping at the government-run girls school in Jogana village, they added.
It is not being treated as suspicious.
Fire-fighters spent seven hours trying to put out the blaze, an eyewitness told the BBC's Hausa service.
The government has closed the boarding school and ordered a full investigation into the fire.
The UN Security Council has authorised the deployment of a UN police force to Burundi to try to quell violence and human rights abuses in the country.
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The mother of Madeleine McCann has embarked on a 500-mile (800km) charity bike ride to raise funds to support families with a missing loved one.
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(Close): London share prices fell back slightly, with the FTSE 100 index closing 20 points lower at 6,710, a fall of just 0.3%.
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At least seven female students have died after a fire at a boarding school hostel near the northern Nigerian city of Kano on Sunday night, officials say.