As long as you stay within the Joomla 4 major version and move from one minor version to its immediately next (e.g. from 4.0 to 4.1) there is no migration necessary. You just need to install the new Joomla minor version (4.1, 4.2, or 4.3) and update Akeeba Backup if there is an update available.
Please keep in mind that we can only reasonably provide an upgrade path from one Joomla minor version to its immediately next minor version, i.e. 4.0 to 4.1, 4.1 to 4.2, 4.2 to 4.3. If you are going to leapfrog one or more minor versions, e.g. go from 4.0 straight to 4.3, there might not be a version of Akeeba Backup compatible with both Joomla minor versions. In this case, please use the procedure outlined below.
We very strongly recommend upgrading your site frequently, to every new minor Joomla version. Moreover, we recommend always using a PHP version which is marked as Currently Supported by the PHP project. This will lead to a no-hassle update experience and a minimum of potential problems when updating your site.
Take a full backup of your site and store it somewhere safely, outside of your web server. Ideally, keep two copies on separate media, e.g. a copy on your computer and a copy on a removable hard drive or USB flash drive.
Your backup may consist of several files with the same name and extensions .j01, .j02, …, .jpa; or .j01, .j02, …, .jps; or .z01, .z02, …, .zip. You must download ALL of these files to have a complete backup of your site.
Whether you have one or multiple files for your backup can be determined by going to Components, Akeeba Backup, Manage Backups. Find the backup record and click on the Download button. If you see a single Download button in it there is just one file (.jpa, .jps, or .zip). If you see multiple buttons there are multiple files.
Go to System, Manage, Extensions and disable the following extensions. Note down which of these extensions were enabled (published) on your site:
Action Log - Akeeba Backup. Plugin.
Console - Akeeba Backup. Plugin.
Quick Icon - Akeeba Backup Notification. Plugin.
System - Backup on update. Plugin.
Task - Akeeba Backup. Plugin.
Do NOT disable the package or component. It will make it impossible to upgrade Akeeba Backup after updating Joomla.
After upgrading to the newer version of Joomla 4 check our Compatibility page for a version of Akeeba Backup which is compatible with your Joomla and PHP version.
If you are not sure about your Joomla and PHP versions please go to System, System Information and look at the PHP Version and Joomla! Version rows.
If the only versions compatible with your Joomla version require a newer PHP version please upgrade the PHP version of your site. Ask your host how to do that.
Go to System, Update, Extensions. Click on Check for Updates. You will see an update for Akeeba Backup; select it and click on Update.
If the update fails to install, go to our Compatibility page and download it. Then go to System, Install, Extensions, Upload Package File and install the file you downloaded, twice in a row, without uninstalling it before or in between.
Go to System, Manage, Extensions and enable the extensions you had noted in a previous step were previously enabled.