The earliest RFC which I know of which spells it out is RFC 805, https://tools.ietf.org/html/rfc805

      It was clear that the information
      content of all these syntactic alternatives was the same, so that
      the one causing least difficulty for existing systems should be
      chosen.  Hence it was decided to add all new information on the
      right of the @ sign, leaving the "user" field to the left
      completely to each system to determine (in particular to avoid the
      problem that some systems already use dot (.) internally as part
      of user names).

   The conclusion in this area was that the current "user@host" mailbox
   identifier should be extended to "user@host.domain" where "domain"
   could be a hierarchy of domains.
      
      In particular, the "host" field would become a "location" field
      and the structure would read (left to right) from the most
      specific to the most general.

As for why 'mailbox' comes first, it's presumably because that's someone's username. The very first thing you want to see is, "I'm sending this to drostie," and only afterwards do you need to know where that server is located.

I don't have any concrete evidence, but my guess is that having the repeating value (the TLD) at the front meant that storing domain names in a hashtable was inefficient. Lookups would be faster if the more-unique part was at the front of the string, since the string comparisons would run faster.