Bain was voted in at Tuesday's AGM, where Lex Gold was unanimously re-elected as chairman.
Dundee United chairman Eddie Thompson, Hibernian chief executive Rod Petrie and Falkirk chairman Campbell Christie continue on the five-man board.
The SPL also announced another television deal, which will see games broadcast on the new BBC Gaelic channel.
The two-year contract will see one SPL game shown in its entirety on the free channel, which launches on September 19.