Open Outlook on your machine, navigate to Home and Address Book
Search for your distribution list, you might need to change the Address Book to the Global Address List (most up to date). Finally select your distribution list/group
You can then see the owner of the group/list. If you are the owner you will have the ability to click modify members to add or remove members.
Click Add… Then search the Global Address list for the users you want to add, select their accounts and click Add and then Ok when you are done
You will now see your member added to the members list, you can press apply and ok to save changes
From the app navigation waffle in the upper-left corner, select the Outlook app, if you are not already there.
On the Outlook ribbon, click on the Settings wheel button. From the drop-down list, click on View all Outlook settings
In the left navigation pane of the Settings page, click to expand the General selection list
From the General list, select Distribution Groups
In the Distribution groups I own section, select the distribution group you want to modify from the list and click the pencil icon. Please note, if the distribution list that you want to modify is not listed, you may not be the list owner or the list may be hidden.
On the Distribution Group window that opens, select membership from the left menu to view members of the list.
¶ To add/remove members to a distribution list that you own
After following the instructions above to view group membership, click on the '+' (plus) button. A new window will open with the Office 365 People directory.
In the directory window, use the Search People function to find the person or people you want to add to your list.
From the Search results, click on the button that corresponds to the person you want to add to the distribution list. The person will be displayed in the Members row. Repeat until all new members have been selected.
Once all new members have been selected and added to the Members row, click Save.
Verify that the new members have been added to the Members list in the Distribution Group window. If no further changes are necessary, click Save.
Click the close button in the upper right corner of the Settings page to return to your Office 365 mail.