Mr Lewis said that the introduction of compulsory anti-bullying policies in schools four years ago had failed to make enough impact on the problem.
His announcement coincided with a poll of 1,000 pupils by the charity ChildLine which showed that two out of three secondary pupils would feel uncomfortable about telling their teacher they were being bullied.
More than half of the primary pupils and a quarter of secondary pupils said they had been bullied this term.
Mr Lewis said headteachers should not be afraid of suspending pupils who had tormented others. He announced a package of measures including changes to school inspections from September, which will encourage inspectors to be tougher on schools that are failing to tackle bullying.
Guidance will be sent to secondary schools on training staff to deal with bullying and on how to consult their pupils on the problem.
Specialist "bullying consultants" for local education authorities, will be introduced as part of a previously announced pound;470 million programme to improve behaviour and attendance Mr Lewis told a conference of his experience of being intimidated between the ages of 11 and 13 at an independent school in Manchester. His misery stopped only after he hit back at one of his tormentors - a fight which left Mr Lewis with a broken nose, but with the respect of other pupils.
"I remember the sense of isolation and loneliness and distressed anger. I remember the feeling in the pit of my stomach every morning as I set off for school. I remember the mental agony involved in controlling my emotions," he said. "I am not advocating the use of physical force to tackle bullying. The scandal is that it was allowed to get to that stage in the first place."
An Office for Standards in Education report on effective ways of tackling the problem recommended including peer support and mediation by pupils.
Inspectors found that three-fifths of schools had good systems for tackling bullying, but that many anti-bullying projects had only a short-term impact.
"Bullying: effective action in secondary schools" is at www.ofsted.gov.uk.
"Tackling Bullying" is at www.childline.org.uk