The Foreign Office changed its travel advice to the country yesterday (January 17) urging against “all but essential travel”on the grounds of the “deteriorating political situation” in the west African nation and the risk of “potential military intervention” following presidential elections in December.
Cook said it planned to return 985 package holiday customers to the UK over the next 48 hours.
The operator added that an additional 2,500 flight-only customers would be offered the "earliest available flight" from the country.
In a statement on its website, Thomas Cook said: "We will operate a programme of additional flights into Banjul airport over the next 48 hours to bring the 985 UK customers we currently have on holiday in Gambia home, including four additional flights on Wednesday January 18.
"In addition, we have approximately 2,500 flight-only customers in Gambia, whom we are contacting to offer the earliest possible flight availability for return to the UK."
Cook said it would be dispatching a “special assistance team” on the first flight from the UK to provide support to customers.
"Our colleagues on the ground in Gambia will proactively contact all customers on holiday with us as soon as possible to prepare for return to the UK," the statement continued.
Specialist operator The Gambia Experience, part of Serenity Holidays, is to run repatriation flights today into Gatwick and a second on Friday. Further flights to Birmingham and Manchester are being organised.
Outbound trips up to January 31 have been cancelled with refunds offered.
Travellers booked with the operator to the Gambia between February 1-15 can amend their travel dates or switch to an alternative destination provided by parent company Serenity Holidays.
“Whilst the current situation in The Gambia remains calm we will be working with the FCO and airline partners to offer pre-emptive repatriation flights back to the UK,” the company said.
Abta said it estimated there are around 2,000 holidaymakers currently on holiday in the country with its members.
The association said it advised package holiday customers to contact their tour operator to confirm arrangements for returning home.
"Package holidaymakers due to travel imminently to The Gambia are advised to contact their tour operator to discuss the options of changing their date of travel, receiving a full refund or booking an alternative holiday," Abta added.
Outgoing Gambian President Yahya Jammeh has declared a state of emergency in the country a day before his official mandate ends, BBC News reports.
Jammeh has claimed "extraordinary" foreign interference in his country’s affairs and in last month’s presidential election.
Regional leaders have been successful at persuading Jammeh to hand over power to Adama Barrow, who won the election.