With regard to extraterrestrial property sales, two treaties exist today.
These treaties do not refer to "ownership" as such, they more commonly refer to the "exploitation of the Moon and other celestial bodies for profit purposes", and extraterrestrial property sales distinctly fall under that section. The treaties are, The Outer Space Treaty of 1967 and the Moon Treaty of 1984.
The Outer Space Treaty of 1967 explicitly forbids any government from claiming a celestial resource such as the Moon or a planet.
What does this mean? Well it means that governments can not appropriate the Moon or other celestial bodies. Effectively, governments have signed to the fact that they have no rights to these bodies at all. What is actually important here is what the Outer Space Treaty does not say. It explicitly does not say whether commercial enterprises or private individuals can claim, exploit or appropriate the celestial bodies for profit. (Note that the Lunar Embassy is not a government body.)
The United Nations and all countries that signed the Outer Space Treaty became aware of this vital omission almost immediately after the treaty was ratified in 1967. In fact, the United Nations have expended a large amount of time trying to ratify an amendment to the treaty ever since, that would explicitly include corporations and individuals. All attempts at ratifying such an amendment failed because member states did not agree with it. So, in the end, all the ratification attempts were summarized into the famous Moon Treaty some 15 years later. This information is a well documented fact today.