The legal definition of a condominium came from the start of the 18th century to describe states owned by more than one country cooperatively. If you look up the term Condo and International Law you will find a list of the current and former territories which were governed as condominiums.

In the US, from what I remember writing insurance for these entities, they started being used in the mid to late 70s - at least in NYC where formerly private rental apartment buildings were bought out and converted into either Condos, or into Cooperative Corps. A coop is similar to a condo in that the units are owned by the coop corporation (not the unit owners) - but the owners of the corp are granted indefinite leases to their individual unit. These concepts were also extended to post-war suburban real estate developments in the form of the HOA.