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:

Competitors aged 14 to 19 are hiking distances of up to 55 miles (89 km) visiting 10 nominated tors over two days.
The 56th event started at 07:00 BST, with 2,400 teenagers - many from school and youth groups from across the South West - taking part.
The first teams are expected to cross the finish line on Sunday morning.
Source: BBC/Ten Tors
The teenagers left Okehampton Camp, where Dartmoor National Park head ranger Rob Steemson said it was an "enormous challenge".
The event is organised by the Army and assisted by the Royal Navy, the Royal Air Force and the Dartmoor Rescue Group.
Each team has a GPS tracker, so safety teams can find out where each group of teenagers is. The tracker also has an emergency button if help is needed.

The city council said developing the Bannerdale site, off Carter Knowle Road, posed no risk to health.
It said it had carried out extensive investigations into any potential risks.
Campaigners have raised concerns over possible health risks and increased traffic if the build goes ahead.
More on this story and others on Local Live Yorkshire
The development, which includes sports facilities and a 1,200 place secondary school, attracted more than 80 objections.
However, Joel Hardwick, Schools Organisation Manager at Sheffield City Council, said: "It's really important to stress that we would never build a school on land that was unsafe.
"We know that it is a suitable and safe place to build an excellent new school to serve the south west of Sheffield."
The authority said the birth rate in Sheffield had increased by 25% since 2002, with 1,000 more children per year entering education.
It said the area earmarked for the school was a popular location for young families and the additional places were needed to meet demand.
Opponents said air pollution and traffic congestion were already a problem in the area and would be made worse by the school, which they claimed was not needed.
They also raised concerns about possible health risks posed by waste from the former landfill site, and the loss of green space.
The plans were approved at a meeting on Tuesday.
The number of children and young people needing counselling about online bullying has increased by 88% over five years, according to a helpline.
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Thousands of teenagers are trekking across Dartmoor in the famous Ten Tors challenge.
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Plans to build a Â£25m school on a former landfill site in Sheffield have been approved, despite concerns over the suitability of the area.