Miscellaneous topics that do not fit into specific categories.
Hello
You cannot add an "existing" outlook.com address to another Microsoft account as username/alias.
Outlook.com is its own Microsoft account already, and you cannot transfer products or subscriptions purchased from one Microsoft account to another.
If your Office product is a subscription, the only way to switch is to cancel it from the gmail Microsoft account, then once it expires, sign up a new one iwth the outlook.com account.
If it is perpetual one-time purchased license, then it is not possible, unfortunately.
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If all you want is just to switch it to an outlook.com address, not a particular outlook.com address, you can consider this:
Sign into your personal account via this link: https://account.live.com
Go to Your Info > Sign in preference, Add an alias.
Create new: this will allow you to use the native domain outlook.com to create a new alias.
You cannot use an existing outlook.com address here though.