I had a similar requirement some time ago. I found it easier to convert EML files to PST format first because Outlook.com doesn't let you import them directly. I had a good experience with Toolsbaer EML to PST Converter and it worked quite well for me. It not only kept all the email details safe but it also converted multiple EML files at once. I exported my EML file to PST and then used Microsoft Outlook's Import/Export tool to import it into Outlook. After I synced my Outlook account with Outlook.com, the emails showed up in my mailbox. If you have batches of EML files then this method is quite easy to use

Read More: https://www.toolsbaer.com/eml-to-pst-conversion/