The former Scotland internationalist has been serving as interim chairman and indicated last month he would be interested in extending his tenure.
Speaking at the second part of the SRU agm, Jeffrey also issued an appeal for unity in a sport that has been riven by infighting in this country.
Ian Barr, the SRU president, welcomed the appointment. He said: “I am delighted that JJ has been approved by the board as chairman. I could not think of a better person to chair Scottish Rugby at this important time.
“I very much look forward to working closely with him and together we plan to deepen our dialogue and engagement with our member clubs in the weeks and months ahead.
“JJ has been a real positive force since his appointment as interim chair back in May and we quickly realised we had an excellent, knowledgeable and highly respected rugby man who could take on the role permanently.”
Jeffrey said: “I am passionate about the game in Scotland and I am proud to be given the unanimous backing of the board to extend my term as a non-executive director and chairman. I am looking forward to working closely with president Ian, the board and council and all our stakeholders to drive the sport forward.”
Jeffrey’s appointment as chairman also sees his underlying term as a non-executive director extended for an equivalent period, taking him up to three years in both roles.
The SRU board has also confirmed the appointment of Shona Bell in her new role as director of people and internal communications (formerly director of HR) to join the board in January 2021.
General counsel Robert Howat steps down from the board with effect from 1 January 2021 to enable him to provide continuing support and expertise to the board, council and executive through his role as company secretary.
The SRU also announced changes to its executive leadership team.
A statement said: “Scottish Rugby’s Executive Leadership Team has also been expanded to include Director of Rugby Development, Sheila Begbie and Director of High-Performance Rugby, Jim Mallinder in a move which formalises the regular operational and strategic input they have been contributing already.
“They join CEO Mark Dodson, Chief Operating Officer Dominic McKay, Finance Director Andrew Healy, Director of People & Internal Communications, Shona Bell to form the organisation’s Executive Leadership Team.
Dodson said: “The last year has given us a chance to see our business differently, make improvements and take a clear view of where we want to be in the future.
“Sheila and Jim ensure we can strengthen our leadership group and that every level of rugby in Scotland continues to be fully represented.”
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