Begbie, a former Scotland football international who once scored against Italy at the San Siro, made the switch to rugby in 2014.
A pivotal figure in the development of women’s sport in Scotland, she has dedicated much of her adult life to football and rugby.
She joined the SRU as head of its women and girls programme, a position she held for three years, before taking on responsibility for the development of the grassroots game in Scotland in 2017.
In the new role, Begbie oversaw a restructuring of the SRU’s rugby development department, creating a new regionalised model of delivery to clubs.
The regionalised network has kept clubs informed and connected during lockdown periods while the grassroots game has been suspended.
Speaking on her decision to retire, the 63-year-old said: “I can honestly say I have had the best years of my career at Scottish Rugby. It has been a hugely challenging and enjoyable experience from the outset.
“I have had fantastic support from the many colleagues I have been fortunate to work with, both in the rugby development department and across the organisation.
“I would make special mention of Scottish Rugby CEO Mark Dodson who has been an unwavering supporter of the work I have done, and his leadership and friendship have been both empowering and supportive throughout.
“My role has enabled me to develop close connections across the clubs and schools in Scotland, with the clubs being the heartbeat of the game, and I would like to pay particular thanks to the army of volunteers who every day give up their time to support the sport they love.
“I hope I have had a positive impact on rugby in Scotland over the past seven years and wish everyone connected with the game well in the years ahead.”
Begbie will remain in post to support the Return to Rugby programme planned to roll out in line with an eventual easing of lockdown and to help the transition process with her successor.
Growing up in the Drylaw area of north Edinburgh, Begbie said she started playing sport “with the boys in the street”.
She joined a football club, Edinburgh Dynamos, and won the first of her 25 Scotland caps only two years later.
Her debut was an 8-0 defeat by England in 1973 but a year later she played against Italy in Milan’s famous San Siro, scoring both for Scotland and an own goal in a 3-1 loss.
Her greatest achievement on the pitch came in 1977 when she captained to the Scots their first ever win over England, at Downfield Park, Dundee. Scotland had to wait 34 years for another victory over the Auld Enemy.
Begbie went on to become head of women’s football at the Scottish FA where she helped grow the game before making the switch to Murrayfield.
Dodson said: “I would like to record my thanks to Sheila for the significant contribution she has made to Scottish Rugby over the last seven years.
“Sheila has made a big difference to our organisation firstly in the women and girls programme and then the Rugby Development department and I’ve greatly enjoyed working with her.”