Enable delete of Field History and Field History Archive

Follow these steps to make the Delete from Field History and Delete from Field History Archive permissions available.

Salesforce Classic and Lightning: 

1. Click Setup.
2. Enter User Interface in the Quick Find box and select User Interface.
3. Under the Setup heading, select the "Delete from Field History" and "Delete from Field History Archive" checkbox.
4. Click Save.

After enabling the permissions above, grant your users the system permissions below via permission set or custom profile.

• Enable 'Delete From Field History'.
• ​Enable 'Delete From Field History Archive'.

Note:

• Field history tracking can be deleted using Data Loader or any other API tool

See Also: 
Delete Field History and Field Audit Trail Data
Configure User Interface Settings  
Field History Tracking and storage   
Use Data Loader to mass delete field history