Farry was born in Glasgow in 1955, attending school in East Kilbride before working as a landscape gardener. In the late 1970s he joined the Scottish Football League and worked his way up to the position of league secretary during a ten year career. During his stint as league secretary, Farry earned a reputation as an efficient administrator and when the position of Chief Executive of the Scottish Football Association (then termed Secretary of the SFA) became vacant in 1990, he was approached as a successor to the departing Ernie Walker.
Whilst Chief Executive, Farry oversaw a number of ambitious projects, such as the renovation of Scotland's national football stadium Hampden Park. The 'new Hampden' as it was termed, drew both support and criticism, with opinion divided over the need for a dedicated national stadium within Scotland. As the stadium is used at club level by Queen's Park F.C., a team currently playing in the Scottish Second Division and possessing limited support, some footballing figures (for instance the Scottish journalist Jim Traynor) had argued that an existing stadium could have served as a home for the Scottish national team indefinitely. Alternatively, supporters of the stadium, such as Farry himself, have pointed to the awarding of UEFA five-star status and the hosting of a number of high profile matches, most notably the final of the UEFA Champion's League in 2002 and the final of the UEFA Cup in 2007, as proof of the renovation's success.
In 1997, Farry attracted criticism from some parts of the media in the aftermath of the death of Diana, Princess of Wales, after he publicly rejected calls to cancel a scheduled international match between Scotland and Belarus on the day of the Princess's funeral. He later revealed that he had been advised by Buckingham Palace to let the game go ahead; however after a hostile reaction from the media and certain sections of society, the match was eventually rescheduled.
On the 8th of March 1999, Farry was sacked for gross misconduct and left his position as Chief Executive after a period of 9 years in the job. McCann and others highlighted the incident as proof of an alleged "institutional bias" against Celtic , though others (e.g Jim Traynor) have explained the incident in terms of a personal animosity between the two men stemming in part from disagreements relating to the Hampden renovation project (Celtic Park being one of the existing grounds which could have served as the new national stadium).