The NSPCC's Childline service said it counselled more than 4,500 children in the past year compared to about 2,400 in 2011-12.
The total number suffering online abuse is thought to be far higher.
Some children as young as seven told Childline how they were tormented, abused and scared to go to school.
The charity said online trolls caused misery and humiliation for thousands of children.
Childline's president Dame Esther Rantzen said the figures should be a wake-up call.
"Bullying can wreck young people's lives, especially now that the bullies don't stop at the school gates," she said.
"Cyber-bullying can follow them home until it becomes a persecution they cannot escape.
"It is imperative that adults, parents and teachers, intervene to protect them, because we have learned over the years from Childline callers that bullying does not stop on its own, left alone it gets worse.
"Schools must take this problem seriously, and above all children must ask for help."
The report is being released at the start of Anti-Bullying Week which is coordinated by the Anti Bullying Alliance.
The group is working with parents, schools and other organisations to help combat the problem.
One young person who contacted Childline said: "It might sound like not much of a problem but there's a group of people I play with online and they told me to kill myself. I won't kill myself but it upsets me.
"My parents don't realise how upset it's making me and they tell me to stand up for myself or just not play anymore but they don't know how hard that is.
"I don't know why they have suddenly started picking on me but it hurts so much."
Advice given by young people on dealing with bullying includes:
The number of children and young people needing counselling about online bullying has increased by 88% over five years, according to a helpline.