The Competition and Markets Authority (CMA) on Tuesday (1 December) confirmed it had secured formal commitments, or "undertakings", from the firm following an investigation.
According to the CMA, many of those awaiting refunds have been waiting more than the 14-day statutory refund window.
Lastminute has agreed to repay at least half of those customers awaiting refunds by 16 December, and the rest by 31 January 2021 at the latest.
Additionally, the commitments secured by the CMA will require Lastminute to ensure anyone due a refund for a cancelled holiday from Thursday (3 December) and beyond will be paid within 14 days.
It must also provide the CMA regular updates on its efforts to refund customers.
Andrea Coscelli, CMA chief executive, said: "Online travel agents have a legal responsibility to provide prompt refunds to customers whose holidays have been cancelled due to coronavirus, irrespective of whether the agent received refunds from airlines and accommodation providers.
"Our action means customers whose holidays were cancelled by lastminute.com will receive their money back without undue delay."
Coscelli added: "The CMA is continuing to investigate package holiday firms following concerns that people are not getting the refunds they’re entitled to when bookings can’t go ahead because of the pandemic.
"If we find that businesses are breaching consumer protection law, we will not hesitate to take further action."
The CMA has written to more than 100 package holiday providers to remind them of their obligations to comply with consumer protection law, securing refund commitments from Virgin Holidays, Tui, Sykes Cottages and Hoseasons parent Vacation Rentals.
A Lastminute.com spokesperson told TTG: "Since March, we made refunding customers our number one priority and we’re pleased to reiterate this commitment with the CMA.
"We engaged constructively with the CMA and while we have already refunded more than €200 million worth of bookings overall, it is the group’s commitment to work through those that remain to be paid.
"After the commitments already taken by Tui UK, Virgin Holidays and other players in the market, our effort highlights how we are actively working on this side. Many other competitors and especially some airlines do not have still reached any factual commitment to act for refunding the customers.
"The entire travel industry is facing an unprecedented crisis including enormous challenges that our systems and processes had to face to manage such a huge volume of cancellations and refunds.
"We appreciate that the CMA has recognised the special circumstances that Covid-19 has created both for many travellers and players from the travel sector."
