The Civil Aviation Authority (CAA) said it has been asked by the Government to charter more than 30 aircraft to bring the passengers back to the UK after the airline failed to renew a crucial licence.
Some 300,000 future bookings have been cancelled as a result of the company's failure, the largest to hit a UK airline, and customers have been told to keep away from airports as there will be no more flights.
CAA chief executive Andrew Haines said: "We know that Monarch's decision to stop trading will be very distressing for all of its customers and employees.
"This is the biggest UK airline ever to cease trading, so the Government has asked the CAA to support Monarch customers currently abroad to get back to the UK at the end of their holiday at no extra cost to them.
"We are putting together, at very short notice and for a period of two weeks, what is effectively one of the UK's largest airlines to manage this task.
"The scale and challenge of this operation means that some disruption is inevitable. We ask customers to bear with us as we work around the clock to bring everyone home."
Customers affected by the company's collapse have been urged to check a dedicated website monarch.caa.co.uk for advice and information on flights back to the UK.
It also gives information to those passengers that have future bookings with Monarch but are yet to leave the UK.
The CAA said all Monarch customers who are abroad and due to return to the UK in the next two weeks will be flown home.
The flights will be at no extra cost to passengers and they do not need to cut short their stay, the regulator said.
The Government has warned passengers to expect disruption and delay as it works to ensure there are enough flights to return the "huge number" of passengers.
Commenting on the "extraordinary operation", Transport Secretary Chris Grayling said: "This is a hugely distressing situation for British holidaymakers abroad - and my first priority is to help them get back to the UK.
"That is why I have immediately ordered the country's biggest ever peacetime repatriation to fly about 110,000 passengers who could otherwise have been left stranded abroad.
"This is an unprecedented response to an unprecedented situation. Together with the Civil Aviation Authority, we will work around the clock to ensure Monarch passengers get the support they need.
"Nobody should underestimate the size of the challenge, so I ask passengers to be patient and act on the advice given by the CAA."