How to import your contacts to Microsoft 365
First to export your current contacts from your mail client into a .csv or pst format.
Microsoft have a guide for doing this in MS Outlook –http://office.microsoft.com/en-gb/outlook-help/export-contacts-HA101870639.aspx
Once you have this exported, then simply log into your Outlook Web Access athttps://portal.microsoftonline.com
Select people as shown below,
Once in people go to Settings >> Import Contacts
Which will open this screen.
Next select the file you exported earlier and click next.