There are different ways to accomplish that. Depend on budget or preferences.
One very popular way is to create an API hosted on premise that allows logic apps to push data to your on-prem resource.
1 is a REST API you can write to connect to your destination resource. Of Course it must be exposed to the internet
If you don't want to write code and keep it more on azure you will need to use one of these approaches to link your on-prem network to azure and make your on-premises resources visible to azure :
Where are you dropping the files? Are you passing to an on prem folder or DB? Large scale? You may find azure data factory is a better fit depending of the scenario:
You can also use SSIS if you are pushing to SQL Server on-premises: https://learn.microsoft.com/en-us/azure/architecture/data-science-process/move-data-to-azure-blob-using-ssis