The CMA said it had been "investigating" Loveholidays after receiving hundreds of complaints that people were still awaiting refunds.
When customers contacted Loveholidays to request a refund for a cancelled holiday, they were told they would only receive money back for their flights once the firm had received refunds from the respective airlines.
Under the Package Travel Regulations, OTAs are legally bound to refund customers for package holidays cancelled due to coronavirus, regardless of whether or not the agent has received money back from suppliers.
Loveholidays has now signed formal commitments – known as undertakings – that ensure these customers receive all their money back by March 2021 at the latest.
More than £18 million will be refunded to 44,000 Loveholidays customers. Of this, so far £7 million has been refunded to 20,000 customers.
Refunds will be made in two parts. Further details of the relevant payment dates can be found on the CMA’s package travel webpage.
To ensure that Loveholidays adheres to its commitments, the company must provide the CMA with regular reports on the progress of its repayments.
If the firm fails to repay customers by these dates, the CMA is prepared to take the company to court.
Andrea Coscelli, chief executive of the CMA, said: “Travel agents have a legal responsibility to make prompt refunds to customers whose holidays have been cancelled due to coronavirus.
“Our action today means that Loveholidays’ customers now have certainty over when they will receive their money back and they will receive this without undue delay.
“We are continuing to investigate package travel firms and where we find evidence that businesses are breaching consumer law, we will not hesitate to take enforcement action to protect consumers.”