His resignation from the Shadow Cabinet will open the way for Ann Widdecombe to replace Sir Norman as shadow Home Secretary in William Hague's next reshuffle.
He famously announced his resignation from the Cabinet under Baroness Thatcher to spend more time with his family in 1990 when he was Employment Secretary. Two years later, he was brought back by John Major as party chairman.
Mr Hague's reshuffle will be wide-ranging to bring fresh faces into the Shadow Cabinet. Those tipped for promotion include Theresa May, the MP for Maidenhead, and spokesman on education; Damian Green, another education and employment spokesman; and Tim Yeo, who resigned from the government over an illegitimate child.
The Conservative leader is expected to carry out the reshuffle after the European elections on 10 June to freshen his team, and to boost his own leadership, if the Tories' Eurosceptic campaign rebounds on the party.
Sir Norman is the third Tory frontbencher to announce he is stepping down, after Gillian Shephard, the shadow Environment Secretary, and Michael Howard, the shadow Foreign Secretary.
Ms Widdecombe, regarded as one of the big hitters in Mr Hague's team, has told friends that she wants to give up her present role as health spokesman to take on the Home Affairs portfolio.
As a junior Home Office minister, she clashed with Mr Howard, then Home Secretary, and in opposition privately vowed not to take on the lead role until he had retired. Mr Howard's departure has left the way open for her to have the job she wants, shadowing Jack Straw.
Like Mrs Shephard, Sir Norman waited until after the local elections to make his announcement, although it was well known that he would step down. "I have spent 20 of the last 25 years as a cabinet minister, shadow minister or party chairman. I told William Hague of my plans to stand down at the beginning of this year. I intend to continue as MP for Sutton Coldfield. My view has always been that the best position of all is being an MP at Westminster.
"I will do all I can to help in the further recovery of the party."
Mr Hague praised Sir Norman's contribution.Reuse content