This document describes how to configure Graylog in order to receive data from ULS. The recommended way is the Raw/Plaintext TCP Input.
Go to System -> Inputs and create a new Input:
As Extractor, you can use the "JSON" extractor using the standard settings.
Eventually it is required to add additional JSON extractors for fields like "event_aupCategories", "query_resolved", ...
Please see the extractor documentation for more help.
See this bug report within the graylog universe.