Speaker William Hay asked the clerk to read out the result of the vote
The devolution of policing and justice powers to Northern Ireland marks the end to decades of strife, Prime Minister Gordon Brown has said.
Out of the 105 votes cast in the NI Assembly, a total of 88 supported the move, with 17 against.
Mr Brown said the politics of progress had now replaced politics of division.
"It sends the most powerful message to those who would return to violence: that democracy and tolerance will prevail," he said.
"The courage and leadership of the parties who voted to complete devolution at Stormont will be noted around the world."
Policing and justice powers will now be devolved on 12 April after a 38-year gap.
US Secretary of State Hillary Clinton said devolving the powers was an important step in ensuring a peaceful and prosperous future for Northern Ireland.
Hillary Clinton had personally lobbied NI politicians
"I encourage all parties to work together in a spirit of cooperation and compromise as they continue the road toward a full and lasting peace," she said.
"The United States stands with the people of Northern Ireland in their efforts to build and sustain a thriving, confident, and shared society."
Disagreement on the timing of the devolution of the justice powers had threatened to collapse Northern Ireland's power-sharing administration.
In February, Northern Ireland's two main parties, the DUP and Sinn Fein, reached an agreement which, now the vote has been passed, will see a justice minister elected.
The Hillsborough Agreement allows for the first and deputy first ministers to identify a candidate who would command cross-community support in the assembly.
As expected, the Ulster Unionist Party voted against the powers being devolved, however, Tuesday's motion received the necessary cross-community consent to be passed.
All 44 of the nationalist assembly members backed the vote, while 35 out of 52 unionists also supported it.
Nine other members, including the Alliance Party's MLAs, also voted in support of the powers being devolved.
DUP leader and Northern Ireland First Minister Peter Robinson accused the UUP of seeking political advantage by voting against the devolution plans.
"I believe it is time for us all to move forward," he said.
"There must be no going back to the bad old days of the past.
"Throughout history there are times of challenge and defining moments. This is such a time. This is such a moment."
UUP leader Sir Reg Empey said his party did not believe the time was right for policing and justice powers to be devolved.
Sir Reg Empey's UUP voted against the motion
"We are a party for the devolution of justice, but it is the conditions to which we are coming," he said.
"We have not had a single solitary discussion at leadership level of what we are going to do with policing and justice.
"It is a bit like doing your driving test without doing your driving lessons."
Sinn Fein's Gerry Kelly described the "overwhelming vote" as a "huge step forward for the people of the north and throughout Ireland".
"It's unfortunate that the UUP were entirely out of line. We will move ahead and it was a huge vote to move ahead on," he said.
SDLP leader Margaret Ritchie said her party's vote for the devolution of policing and justice powers was not an endorsement of the Hillsborough Agreement.
She said: "The SDLP still had serious concerns about the integrity of the process and the gerrymandering of the justice ministry."
Alliance leader David Ford said it had been a momentous day for Northern Ireland.
"This is the start of the process which will see politics here come of age," he added.
Conservative Party leader David Cameron said his party had long supported the devolution of policing and justice powers.
He said: "Concerns about the functioning of the executive as a genuine four-party coalition prevented the Ulster Unionists from backing today's vote, and I hope these will now be resolved in a spirit of genuine partnership."
Irish Prime Minister Brian Cowen said it was a good day for the island of Ireland.
"For the first time, we can look forward to policing and justice powers being exercised by democratic institutions on a cross-community basis in Northern Ireland," he said.
PSNI Chief Constable Matt Baggott said devolving the powers would help achieve a peaceful society in Northern Ireland.
"It will help to ensure that communities receive the policing service that not only they deserve, but that we are committed to delivering," he said.
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