Ansible is an absolutely free and open source tool that is used for the above-mentioned purposes. Because Ansible adopts the standard GNU (General Public License), it can be used for commercial purposes as well as long as one respects the policies of GNU.
The CLI based usage is free with no limits.
Ansible Tower offers free for handling up to 10 nodes. Anything more than that might require a paid license. Ansible Tower provides a neat graphical user interface with a dashboard using which one can group the hosts, variables, jobs, etc.
Ansible AWX is free i.e an open source upstream project for Ansible Tower.