Some 150,000 tourists are being brought home over the next two weeks in a Civil Aviation Authority (CAA) flight programme costing £100 million.
The first rescue flight touched down at Gatwick from Split, Croatia, shortly before midday, and around 15,000 passengers were expected to travel on 61 flights by the end of the day.
Forty-five aircraft from as far away as Malaysia have been chartered to operate approximately 1,000 flights from 53 airports in 18 countries over the next two weeks.
Holidaymakers already abroad are being flown home at no extra cost as close as possible to their original return time and date.
All future Thomas Cook bookings have been cancelled, affecting around one million people.
Lucy Jessop, from Hull, was due to return from a two-week holiday in Mexico on a Thomas Cook flight on Tuesday.
She said she was "initially worried" about the situation but was relieved that alternative flights are being arranged.
"It's the employees of Thomas Cook and all those due to go on holiday I feel for," she added.
"We were the lucky ones, I suppose."
Among those awaiting to hear the outcome of their booked trip are Lewis and Amy Bromiley, from Manchester, who paid £7,000 for a January honeymoon in the Maldives.
Mr Bromiley, 25, told the PA news agency: "Me and my wife are devastated."
He added: "We'll have to wait for the refund which could take months."
Richard Moriarty, chief executive of the CAA, said the Government had asked his organisation to launch "the UK's largest ever peacetime repatriation".
The £100 million bill will be met by the Government and the Atol scheme, which provides protection to customers on package holidays when travel firms collapse, although passengers who made flight-only bookings with Thomas Cook are also being brought home at no extra charge.
Thomas Cook package holiday customers will also see the cost of their accommodation covered by Atol.
Those who have not yet started their package holiday will be given a refund, while those on flight-only bookings are advised to seek reimbursement from their credit or debit card provider, or make a claim through their travel insurer.
Thomas Cook ceased trading in the early hours of Monday morning after failing to secure a last-ditch rescue deal of an extra £200 million needed to keep the business afloat following a full day of crucial talks with its major shareholder and creditors on Sunday.
Unions representing its staff, of which there are 9,000 across the group in the UK, had previously urged the Government to intervene financially.