The Prime Minister said unionists in particular would want to ensure that the "clear statement of principal is kept to in practice."
But speaking in 10 Downing Street, Mr Blair said: "This may be the day which finally after all these false dawns and dashed hopes peace replaced war, politics replaces terror on the island of Ireland."
Mr Blair said: "I welcome the statement of the IRA that ends its campaign. I welcome its clarity.
"I welcome the recognition that the only route to political change lies exclusively in peaceful and democratic means.
"This is a step of unparallel magnitude in the recent history of Northern Ireland.
"The Unionist community in particular and all of us throughout Ireland and the United Kingdom will want to see this clear statement of principle kept to in practice.
"The instruction of the IRA statement that volunteers must not engage in any other activity whatsoever will be taken as a forthright denunciation of any activity, paramilitary or criminal."
The Prime Minister said decommissioning must happen as soon as possible and be verified.
But he said: "The statement is of a different order to anything before.
"It is what we have striven for and worked for throughout the eight years since the Good Friday Agreement.
"It creates the circumstances in which the institutions can be revived.
"Unionism will want to know that these circumstances are permanent and verified.
"But if in time they are, then proper, devolved democratic government should be restored to Northern Ireland."
Fundamental disagreements about the past would remain, Mr Blair said.
"The IRA believe that their means were justified. The rest of us do not and we will remember today the many thousands of victims of their campaign.
"But the best way to serve the memory of those victims is to make the future brighter and there is, at least, some hope today that the future will indeed be such as to banish the ghastly and futile violence from Northern Ireland forever."
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