As long as you stay within the Joomla 3 major version and move from one minor version to its immediately next (e.g. from 3.8 to 3.9) there is no migration necessary. You just need to install the new Joomla minor version and update Akeeba Backup if there is an update available.
Please keep in mind that we could only reasonably provide an upgrade path from one Joomla minor version to its immediately next minor version, i.e. 3.8 to 3.9, 3.9 to 3.10. If you are going to leapfrog one or more minor versions, e.g. go from 3.6 straight to 3.10, 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.
Go to Extensions, Manage, Manage (or Extensions, Manage, Manage Extensions in older versions of Joomla 3) and disable the following extensions. Note down which of these extensions were enabled (published) on your site. Please keep in mind that you may NOT see all of these extensions and that the list of extensions below only includes the extensions shipped with Akeeba Backup versions 4.7.7 and later.
Action Log - Akeeba Backup. Plugin.
Akeeba Backup Lazy Scheduling. Plugin.
Installer - Akeeba Backup Professional. Plugin.
Quick Icon - Akeeba Backup Notification. Plugin.
System - Akeeba Backup Update Check. Plugin.
System - Backup on update. Plugin.
System - One Click Action. Plugin.
System - System Restore Points. 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 3 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.
We only ever supported updating Akeeba Backup between successive major versions, e.g. version 3 to 4, version 4 to 5 and so on. We never supported skipping one or more major versions altogether!
If you find yourself in a situation where you would be leapfrogging a version, e.g. upgrading from Akeeba Backup 5 to Akeeba Backup 8 (skipping versions 6 and 7) DO NOT PROCEED. In this case you will have to completely uninstall Akeeba Backup and only then should you try to install a new version. Do note that this will remove all your backup records and backup archives. You may have to download your old backups before upgrading Akeeba Backup.
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 Extensions, Manage, Update. Click on Clear Cache and Find 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 Extensions, Manage, Install, Upload Package File and install the file you downloaded, twice in a row, without uninstalling it before or in between.
Go to Extensions, Manage, Manage and enable the extensions you had noted in a previous step were previously enabled.