You can create a Systemd unit file in /usr/lib/systemd/system/<service_name>.service. Here is a template:
[Unit]
Description=<description_string>
[Service]
WorkingDirectory=<working_directory>
Type=forking
ExecStart=/bin/bash <absolute_path_to_script>
KillMode=process
[Install]
WantedBy=multi-user.target
Replace anything in the angle brackets with your specific information. The 'WantedBy=multi-user.target' is the magic that tells Systemd to run your script on each start.
On the command line, tell Systemd to enable your service:
systemctl enable <service_name>.service
The next time you reboot your script should be run. Logs will be written to /var/log/messages.
Fedora has some basic documentation on unit files: Systemd unit files