The fearsome flanker became a Lion in 1989 and went on to play a key role in Scotland's Grand Slam winning side the following season.
He won 40 caps for his country between 1984 and 1991, playing in a World Cup semi-final along the way and establishing himself as one of the most-respected back-row forwards in the game.
"I have been looking for a role in rugby since my retirement as Scotland under-20 team manager 15 months ago and when I saw the Scottish IRB representative advertised I was immediately excited," Jeffrey, who had to apply for the post alongside a number of other candidates despite his hefty reputation, told Scottishrugby.org.
"I see it as an extremely challenging position but one which, with my background, I think I can well represent Scotland's viewpoint at the highest political table.
"It is a great honour to be appointed as the Scottish IRB rep and one where I will strive to continue the good work that has been done by the previous IRB representatives. In particular I am looking forward to working with Bill Nolan and benefiting from his great experience."