Members of the British Airline Pilots Association (Balpa) were due to walk out on Friday, for three days from October 12 and four days from October 19.
The pilots have already held one 12-hour and one 24-hour strike after accusing the company of failing to put forward an acceptable pay offer.
Nine days of talks were held at the conciliation service Acas.
Balpa general secretary Brian Strutton said: "Our members voted to end this dispute by binding arbitration, which Thomas Cook has now agreed to.
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"I am pleased that we have been able to find a peaceful way of resolving the pilots' pay dispute without further disruption to passengers."
Thomas Cook said in a statement: "We remain keen to resolve this dispute in the interests of all involved and we will now focus on proceeding with the arbitration process."