Mr Blunkett announced the move when he addressed the Prison Officers Association (POA) annual conference at Southport.
The deal, long campaigned for by the trade union, is likely to be tied in with government demands for a radical review of working practices.
Measures banning prison officers from taking industrial action were introduced by the previous Conservative government in 1994 under the Criminal Justice and Public Order Act.
Prison officers have complained they are facing ever more difficult jobs in the face of a rocketing jail population.
Mr Blunkett was given a standing ovation by delegates, a far cry from the booing which greeted Home Office minister Beverley Hughes last year.
The home secretary was given a warm applause as he took to the stage and immediately announced that he planned to scrap the law.
Mr Blunkett said when the applause died down: "I can tell from the reaction this is long overdue.
"I really do believe that we can have a new beginning and we can do it together."
Mr Blunkett paid tribute to the professionalism of prison officers.
He said it was vital to continue the improvements in the education of prisoners and for that work to continue when they were released from jail.
He said it was a challenge to make sure the work done inside prison was not then undermined by a failure to continue the work outside.
Mr Blunkett said everyone realised the "enormity of the challenge" of the drugs problem in prisons.
"We have seen the tremendous drop that's taken place in the random testing programme, which tests those in prison," he said.
"There's room for improvement to stop these drugs getting under the walls and over the fences."
The home secretary also spoke about the longer sentences he has proposed for those committing the most serious of crimes.
"I make no apology for having announced that life means life," said Mr Blunkett.
He said members of the public were "horrified to see people released even for the most heinous crimes".
Mr Blunkett told delegates that he realised there was overcrowding in prisons, making life more difficult for prison officers.
He said he was keen to improve the induction process which will "help overcome the tragedy of young men and women who have committed crimes taking their own life".
The home secretary said he hoped the prison officers and the Home Office would work together and put their past difficulties behind them.
"I believe that what we are trying to do is have a prison service fit for the 21st century often in conditions built in the 19th century."
Mr Blunkett then touched on the delicate subject of prison officer's pay and said he hoped long-term pay improvements could be put in place.
He was then given a standing ovation from the delegates.
Home Office minister Beverley Hughes was booed by POA delegates when she appeared at last year's conference.
The POA was accused of orchestrating the heckling after it sent out a press release the night before the minister's appearance announcing that she would be booed.
However, a change in POA leadership has since brought better relations with the Prison Service and ministers.
The union has also agreed to a voluntary no strike agreement, which is likely to form the basis of the new deal.
England and Wales now jail more people than any other country in western Europe.
Last week the number stood just below an all-time high set earlier this year of 73,000.
