The company has been criticised for its treatment of the family of Christi and Bobby Shepherd, who died from carbon monoxide poisoning in 2006.
Harriet Green, the firm's former chief executive, said she will donate a third of her shares to charity.
An inquest ruled the pair were unlawfully killed.
The children, from Horbury, near Wakefield, were on holiday with their father, Neil Shepherd and his now wife, Ruth, when they were poisoned by a faulty gas boiler at the Louis Corcyra Beach Hotel.
Ms Green said reports that she refused to meet Christi and Bobby's parents to apologise were false.
She also said claims she had started the process to seek damages over the incident for Thomas Cook were also false.
Ms Green is due to receive seven million Thomas Cook shares, currently worth around £10m.
She said: "I have now reached out to the parents of Bobby and Christi Shepherd.
"On the basis that Thomas Cook are due to give me seven million shares in July, I have told the parents that I will donate one third of that seven million to a charity of their choice."
In 2010 three people, including the manager of the Louis Corcyra Beach Hotel and two members of staff, were found guilty of manslaughter by negligence and sentenced to seven years in prison.
Eight other people were cleared, including two Thomas Cook travel reps.
The inquest heard the faulty boiler had been housed in an outbuilding attached to the side of the bungalow where the family had been staying.
The children's mother Sharon Wood and their father Mr Shepherd had previously criticised the tour firm for not apologising to them directly during the two-week hearing in Wakefield earlier this month.
After the inquest, the company's chief executive Peter Fankhauser said it had not handled its relationship with the family well.
He said: "During the past nine years, we failed to show the compassion that we should have shown to the family."
Last week, the firm revealed it had donated £1.5m to the children's charity Unicef. The money was the remainder after legal costs of a £3m damages settlement from the Greek hotel.

Amateur metal detectorists Jim Wills and Dennis Hewings first unearthed the coins in Ipplepen, Devon, in 2009.
Now archaeologists have uncovered a Romano-British settlement which had trade links to the rest of the Empire.
Dr Sam Moorhead, from the British Museum, said the site raised "a whole series of new questions" about Roman Devon.
The Ipplepen Archaeological Project, which began its 2016 fieldwork just two weeks ago, has involved the University of Exeter, the Portable Antiquities Scheme run by the British Museum, Devon County Council and Cotswold Archaeology.
Until now there was little evidence of the Romans outside of Exeter, which is 20 miles north-east of Ipplepen.
It had been thought that rural areas had not been particularly affected by Roman influence, a spokesperson for the University of Exeter said.
However, the discovery of "significant amounts" of Roman pottery made in other parts of the Empire and imported into Britain has demonstrated the rural site's connections to the rest of the Roman world.
"The presence of these kinds of vessels demonstrates that the people living here... adopted Romanised ways of eating and drinking" including "a taste for Mediterranean products such as wine and olives", Danielle Wootton, the Devon finds liaison officer for the Portable Antiquities Scheme, said.
But the site was "puzzling" when compared to other known settlements in neighbouring counties such as Somerset, where a greater amount of coins, brooches and pottery had been found, she said.
"We are wondering whether the Dumnonii, the tribe who lived in the area now known as Devon, still retained their traditional identity rather than becoming entirely Romanised", Ms Wootton said.
In previous years the team have discovered a Roman road, as well as pot holes which had been repaired.
"Until recently, who would have thought that Ipplepen village was once 'plugged in' to the Roman empire?", Ms Wootton added.
The ex-boss of Thomas Cook is to donate part of her share payout to a charity chosen by the parents of two children who died on holiday in Corfu.
[NEXT_CONCEPT]
The boundaries of the Roman Empire have been expanded following the discovery of Roman coins in a rural village.