Deputy First Minister Kate Forbes previously urged the company to avoid redundancies if they decided to close the centre.
She met senior management and asked them to consider all available options that could remove the need for redundancies.
A spokeswoman for H&M said: “We constantly evaluate how we operate to ensure that we deliver on our goals and contribute to the overall success of the company.
“Having looked into the scope of our customer service set-up, increased competition in the market, our customers changing behaviours and expectations and operational costs, we have made the difficult decision to proceed with the proposed closure of our customer service site in Edinburgh by the end of the year.”
The firm shut 250 stores globally in the aftermath of Covid-19 outbreak, as the pandemic had moved more shoppers online.
A Scottish government spokesman said: “This is a concerning time for employees and their families.
“The Scottish government has engaged with H&M in an attempt to mitigate the impact of the closure and our Partnership Action for Continuing Employment service is already working with staff.”