Microsoft recently announced that. In the announcement, they also revealed a welcome new feature for users who send e-mails from other accounts in Outlook.com. In the past, e-mails sent from Outlook.com would say, "on behalf of," so there was no way to hide the originating Outlook.com account. Now you can send e-mails from other accounts that look exactly as if they were sent from the originating e-mail service provider (Gmail, Yahoo Mail, Comcast, etc.). Here's how to set it up:
Step 1: Go to Settings > More mail settings. Under the "Managing your account" section, click on "Your email accounts." Scroll to "Add an email account, then click on the "Add a send-and-receive account" button.
Step 2: Enter your e-mail account information, including e-mail address and password, then click Next. If you're having trouble getting Outlook.com to log in to your other e-mail account, click on the link to "Advanced options." From here, you can set specific POP3 and SMTP server settings. Keep in mind that in order to add a Gmail account, you'll first need to enable POP download from your Gmail account first. Also, if you're using two-step verification, you'll need to create an application password to use with Outlook.com.
Step 3: Once you've successfully logged in to your other e-mail account with Outlook.com, you'll be asked to choose where you want the e-mails to be saved. Choose a new folder or an existing one, then click "Save."
Step 4: After your e-mail account has been added, click on the "Go to your Inbox" button.
Now when you begin composing a new message, you can click on your name to open a drop-down list of e-mail addresses you can use.
That's it. If you want the default "From" address to be the account you just added, go back to settings where you added the new account and scroll all the way to the bottom. You'll find a drop-down menu of accounts than you can choose as your default "From" address.