Direct debit customers will be refunded within 14 days, but others will have to wait up to 60 days, according to the Civil Aviation Authority (CAA).
A new online refund system will be launched by the regulator on 7 October.
Customers looking to get back funds lost due to cancelled flights or holidays linked to the collapse of Thomas Cook will have to fill out an electronic refund form.
The CAA is having to refund 360,000 customers.
The pool is three times larger than any previous refund programme.
A statement from the authority said: "We hope to pay refunds within 60 days of receiving a valid refund form.
"More information will be available on our website from 7 October."
A total of 100,000 Thomas Cook customers paid for their future holiday by direct debit.
The remaining 265,000 paid through other means and are the ones facing up to a two-month wait to get their money back.
In previous cases where a holiday firm has collapsed the refund process has typically taken from 20 to 30 days.
However, the elevated risk of fraud and the high number of customers involved has delayed the refund process when it applies to Thomas Cook
The CAA has meanwhile brought home more than two thirds of the people who were on holiday when the travel firm collapsed on Monday last week.
There are still more than 43,000 people on holiday abroad who are due to return home on or before 6 October.
Richard Moriarty, chief executive of the CAA, said: "The scale and complexity of this operation will inevitably cause some inconvenience and disruption and I would like to thank holidaymakers for bearing with us."
Peter Fankhauser, the former boss of Thomas Cook, has said he is "deeply sorry" over the historic travel firm's liquidation.
The 178-year-old travel firm collapsed last week, putting 9,000 staff in the UK out of work.