In the community settings, under the Users tab, the community owner is able to add other owners (only option when the community is public), invite other users to join (when the community is moderated or restricted). An owner is not able to add a person as an owner if the one is already a member of the community.
Users tab in a moderated community
Users will receive notifications when they are invited to be owners of a community. They can accept or reject the invitation directly from the notifications center.