Apple has no _formal_ account merging or transferring process. Apps and media bought with one ID are permanently associated with that ID. Look into using Family Sharing to continue to be able to use items purchased with one Apple ID with other Apple IDs, and for some data sharing features.
- Family Sharing - What is Family Sharing? - Apple Support
- Set up Family Sharing - Set up Family Sharing - Apple Support
Share folders with iCloud Drive --> Share files and folders in iCloud Drive on iCloud.com - Apple Support
Read How to use Shared Albums in Photos on your iPhone, iPad, and Mac - Apple Support about how to share photos.
The next section may sound tricky but it lets you merge some things on a device where you have already signed in with an old account but want to use a new account and incorporate data that is already on the device from the old account. Incidentally, the data will then propagate to other devices using iCloud with that new ID. (I haven't tried this with a computer but it may also work with a computer account signed into an old ID.)
If you have signed into the first ID on a device then fortunately when you sign out of that ID it asks you if you wish to retain the data from the old ID on your device (toggle the ones you want to on). If you keep data on the device then when you sign in with the other ID it will merge this data with the account signing into the device. You can later delete individual items from the old ID that you do not want. Similar information can be found in this post I have 2 apple IDs i want to merge them h… - Apple Community Note that only content physically present on the device like contacts, photos and videos will be retained. Meta data such as a game play scores that are tied to a specific ID or are only on a vendor's database remotely, will not be retained. Also turn off storage optimization before doing this. With Optimize Storage, smaller, space-saving photos and videos are kept on your device while all of your original, full-resolution versions are stored in iCloud. Make sure photo optimization is turned off so the full quality versions from the old account are actually on the device before merging the content into your new account. Manage your photo and video storage - Apple Support You can turn optimization back on again once you are fully using your new ID on the device.
Even though apps may remain on a device and may work for a while, you will not be able to update them or redownload them unless you buy them again with this ID or download them with this ID using Family Sharing.
Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac --> Sign out of iCloud on your iPhone, iPad, Apple TV, or Mac - Apple Support
If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.
Click on this link to learn how to 'Sign in with your Apple ID' --> Sign in with your Apple ID - Apple Support
Additional community member posts:
- Apr. 2018 post by ASC helper Winston Churchill on transferring data from one Apple ID to another. Can I merge two iCloud accounts - Apple Community
- Feb. 2021 tips from Eric Root Apple ID - Apple Community
