Yes, it is possible. In Windows, this is what I see when there is a new version available:
When you click the Upgrade Automatically button, Jenkins downloads and install the new war file itself.
Please, check Jenkins wiki for further details. There are some problems if you installed Jenkins from a Debian package.
If you run Jenkins with java -jar ...
I found out via this StackOverflow question which pointed me to JENKINS-27624 which indicates that Java 8 is now required.
Update: I upgraded Java on all my nodes this morning and they are up and working.
For tools which don't offer access to a source code management repository that you can automatically query for updates you could start with a manual trigger, then take a closer look for how is that trigger activated by humans and maybe automate the task:
there could be upgrade email notifications sent to a subscriber list. An automatic email processing ...
From your list of tools:
Jenkins and Github have apt/yum repositories you can use to install and upgrade.
For Atlassian products, best up to date information about repositories I can found is This ShipIt experiment and it seems unlikely to change from this forum post
The workaround may be parsing the mailing list to update the deploy.
Now if you really ...
I recommend Chocolatey. There are more and more companies that are adopting this. For example, if one would like to install Gradle and navigates to the installation page:
Chocolatey is “the package manager for Windows”.
$ choco install gradle
You can overwrite the existing jenkins.war file with the new one and then restart Jenkins.
This file is usually located in /usr/share/jenkins.
If this is not the case for your system, in Manage Jenkins -> System Information, it will display the path to the .war file under executable-war.