How to automatically remove completed Kubernetes Jobs created by a CronJob?

You can now set history limits, or disable history altogether, so that failed or successful CronJobs are not kept around indefinitely. See my answer here. Documentation is here.

To set the history limits:

The .spec.successfulJobsHistoryLimit and .spec.failedJobsHistoryLimit fields are optional. These fields specify how many completed and failed jobs should be kept. By default, they are set to 3 and 1 respectively. Setting a limit to 0 corresponds to keeping none of the corresponding kind of jobs after they finish.

The config with 0 limits would look like:

apiVersion: batch/v1beta1
kind: CronJob
metadata:
  name: hello
spec:
  schedule: "*/1 * * * *"
  successfulJobsHistoryLimit: 0
  failedJobsHistoryLimit: 0
  jobTemplate:
    spec:
      template:
        spec:
          containers:
          - name: hello
            image: busybox
            args:
            - /bin/sh
            - -c
            - date; echo Hello from the Kubernetes cluster
          restartPolicy: OnFailure