Members of the British Airline Pilots' Association (Balpa) took industrial action earlier this month in what was the first UK pilots' strike in over 40 years.
The strike is going ahead after several days of talks under the auspices of the conciliation service Acas failed to break the deadlock.
Balpa has also announced two further 24-hour strikes on September 29 and October 6 should an agreement not be reached.
General secretary Brian Strutton said: "Tortuous negotiations at Acas have failed to resolve the pay dispute.
"Whilst both sides have compromised there is still a considerable gap. Regrettably this means the strike goes ahead.
"We understand this strike will affect people's travel plans, something which we deeply regret.
"Balpa has given ample warning to enable Thomas Cook to change its schedules and minimise passenger disruption. I have also offered strike dispensations to help out in the hurricane hit Caribbean. Our argument is not with passengers.
"We need Thomas Cook to understand just how resolute pilots are and how frustrated they are with the company.
"We urge the company to come back to the negotiating table with a better offer so this situation can come to an end."
A Thomas Cook spokesman said: "We are disappointed that Balpa has decided to go ahead with the strike.
"Thomas Cook management has put forward an increased offer in recent days and remains open to negotiate further.
"We urge Balpa to come back to the table to resolve this issue in the interests of all involved.
"Meanwhile, our priority is to make sure all of our customers can travel with minimum disruption during the strike period.
"We have drawn up robust contingency plans and are pleased to confirm that all of our flights scheduled today will operate."