An architect by profession, Beg was appointed to the FRU Board late last month by the Prime Minister Frank Bainimarama, who is also President of the rugby union.
He succeeds Francis Kean, who stood down as Chairman two weeks ago following a controversial five year term, in which he was accused of homophobia and interfering with team selections.
Kean, a former navy commander who was convicted of manslaughter in 2007, is also a brother in law to Bainimarama.
New chair, Conway Beg, was an assistant coach of the Fiji men's national team which won the Pacific Rim Championship in 2001.
He previously coached the Fiji Under 21 team to an upset win over Australia in 1998 and steered the Fiji Presidents XV to a win over Italy in 2000.
Beg, who has a long association with the Suva Rugby Union, has been involved in all aspects of the game from primary schools through to national level, and said he was fortunate to lead Fiji's biggest sports organisation.
"I am indeed grateful to the Honorable Prime Minister and President of Fiji Rugby, Mr. Voreqe Bainimarama for appointing me to the Fiji Rugby Board and also to the Directors of such Board to show support and to elect me as the Chairman." he said.
"I take this opportunity to thank the outgoing Chairman, Commander Francis Kean for all the achievements and working tirelessly to realise these, and the huge momentum that Fiji Rugby has achieved on the World Rugby stage."
Fiji Rugby Union Chief Executive John O'Connor said Beg's inclusion on the FRU Board will add stimulus and momentum to the development of rugby in Fiji.
"Mr Beg will further the legacy of the Board and I am certain that under his Chairmanship, we will continue to strive to move Rugby in Fiji forward from where we are at the moment and aspire for world standards both on and off the field," he said.
In addition to his new role on the Fiji Rugby Board, Beg also sits on the Boards of the Building Permit Evaluation Committee and Fiji Association of Architects Task Force.