Two separate extensions to the existing building will be created in order to provide more storage space for the clothing company.
A report stated the company needs the extra floor space as business continues to grow.
It added that the company wishes to remain in Barnsley.
The distribution centre was opened last year and employs about 1,500 people.
A spokesman for Asos said the company were delighted, and the move could eventually lead to more jobs.
He added: "As the company gets bigger, we will be looking to take on more staff."