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The turn out was reported to be 59% of the 1,030,084 electorate, although less then 1% of Catholics voted. The Unionist victory has been welcomed by Brian Faulkner, leader of the Unionist Party and by the Unionist MP Reverend Ian Paisley.
The result comes as ten people are being questioned at Ealing police station in west London in connection with a series of bomb attacks in London yesterday.
The eight men and two women are said to have been arrested on their way to Heathrow airport yesterday morning.
The Provisional IRA has admitted it was behind the bomb blasts - but Scotland Yard says it is not completely satisfied the explosions were the work of the IRA.
The Home Secretary, Robert Carr, told MPs there was no evidence to suggest the bombings were connected to the border poll.
The Northern Ireland Secretary, William Whitelaw, said the bombings would make no difference to the publication of a white paper on the future of the province.
Ulster Unionist leader, Brian Faulkner, welcomed the result: "This is the first time ever that the people of Northern Ireland through the ballot box have quite simply and democratically stated their constitutional wishes."
"They have said so clearly today they are determined to stay within the United Kingdom so this removes any argument about our constitutional position from the lips of politicians for good and all, not just for five or ten years."
Gerry Fitt, leader of the opposition SDLP, said the poll result was entirely predictable. He said his party had organised the boycott of the poll because it feared it would lead to an escalation in violence.
He said: "I think on the figures I have just seen, which have just arrived from London, there has been massive impersonation of votes by the unionist party."
Northern Ireland Secretary, William Whitelaw, said everyone had been given the opportunity to vote - it was up to individuals to choose whether they used it or not.