Robertson was voted as one of three top-flight representatives along with Hamilton chairman Les Gray and Ann Budge of Hearts, who retains her place on the board.
Morton chief executive Warren Hawke and Martin Ritchie of Falkirk are the Ladbrokes Championship delegates while Stranraer chairman Iain Dougan will represent the bottom two divisions.
The new-look board will retain only three of last season’s nine appointees - Budge, SPFL chief executive Neil Doncaster and independent non-executive director Karyn McCluskey, who is chief executive of Community Justice Scotland. Murdoch MacLennan is replacing outgoing chairman Ralph Topping on August 1.
The board members were meeting for the first time on Monday afternoon following the organisation’s annual general meeting in the morning.
Gray, Budge and Robertson, who was previously on the Scottish Premier League board while a Motherwell director, emerged from a list of candidates also featuring Dundee managing director John Nelms. The Rangers director had initially stood for election last season before dropping out late on.
Hibernian chief executive Leeann Dempster stood down after representing the Championship clubs last season while Celtic chief executive Peter Lawwell and Partick Thistle managing director Ian Maxwell did not stand for re-election, instead joining the professional game board of the Scottish Football Association.
Brechin’s Ken Ferguson lost out on the Championship vote after his team were promoted while Dumbarton’s Les Hope and Graham Peterkin of Ayr also missed out.