Update, in new office 365 UI:

Server name: smtp.office365.com
Port: 587
Encryption method: TLS

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1. Login in to the Microsoft Online Services Portal.
2. Click on Outlook.
3. Click on the question mark icon in the upper right corner of the page.
4. Click on About.
5. There will be a section titled External SMTP setting that will contain the server name, encryption type and port. You will be able to use those along with your username and password to send email from devices/programs.