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.
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.