Click the "+" button in the upper right corner of the Members page and select Add multiple members from the drop down. 

In the Add members box, choose another group. 

On the next page, select the group where you are an administrator that contains the members you want to add. Use the list to select the desired members and then click Add members. 

Finally, you will be asked if you want to notify the members with an email address that they have been added to the group. Doing so will add the members and then take you to a customizable announcement with those members as recipients.

Regardless of the way you add members, all new members will immediately be sent email or text message notifications for all group activity.