The Competition and Markets Authority (CMA) launched an investigation into the business in April amid concerns that it did not always provide customers with the refunds or other forms of redress they are legally entitled to.
In August, the CMA warned that it could be taken to court if it failed to change its ways.
It had highlighted concerns that Groupon was not responding “satisfactorily to customer complaints” and was not always giving customers appropriate refunds.
It flagged cases where customers had not been provided with the goods or services that they had paid for but were given Groupon credits instead of refunds.
The CMA also said there were concerns the company was failing to ensure the accuracy of product descriptions or that sufficient items were in stock.
On Friday, the regulator confirmed that Groupon will now offer refunds to certain customers who had not previously been offered them.
It added that the discount business has signed formal commitments which will include acknowledging complaints within 24 hours, ensuring accurate descriptions of items and conducting mystery shopping exercises.
Andrea Coscelli, chief executive of the CMA, said: “So much of business relies on trust.
“It’s essential that people shopping online receive what they ordered and are supported if things go wrong, quickly receiving any refund they are due.
“We welcome that Groupon has now committed to address concerns about customer service issues and ensure it is abiding by the law, so that people can feel more confident shopping online in the future.”