Robertson left Fir Park in January after more than a decade there when Les Hutchison completed his takeover of the Lanarkshire club.
Now he will assume responsibility for running Rangers on day-to-day basis more than three months after the previous directors there were overthrown.
Rangers have been operating without a chief executive since March, when Derek Llambias was suspended then removed from the position and from the board.
Robertson has extensive experience in football in Scotland having previously sat on the former Scottish Premier League’s board.
A chartered accountant with PricewaterhouseCoopers and Ernst and Young, he was elected to the SPL board along with Celtic’s Eric Riley in 2010, occupying the position for nine months.
Glasgow University graduate Robertson’s appointment comes a day after Mark Warburton and Daivd Weir arrived at Ibrox as Rangers’ new management team.