The pair faced questions from three members of the newly-formed board. No other candidates were considered in what is a straight fight between the two.
The SPFL came about following the merger of the Scottish Premier League and Scottish Football League bodies.
Longmuir had been SFL chief executive while Doncaster held the same role with the SPL.
Scotland's new league body will govern the country's four senior divisions, with the amalgamation effective from this summer.