Mr Irvine, who was appointed as a trustee in May 1990 and made chairman in October 1995, will be succeeded by Bryan Leask who was elected by his fellow trustees at an SRT meeting on Wednesday night.
“Sport in Shetland has evolved a great deal in the last 25 years and I am privileged to have been able to contribute what I could to that,” said Mr Irvine.
“I retire in the re-assuring knowledge that the trust is in the hands of its very capable staff and trustees.”
Mr Leask, who has served as a trustee since 2010, said: “I’m honoured to have been elected as chairman and look forward to the challenges of building on Joe’s legacy for the benefit of folk in Shetland.”
Mr Leask has been closely involved in the development of rugby in the islands, and coaches the senior team. He is the chief executive of Hjaltland Housing Association.
When Mr Irvine was appointed as a trustee in 1990, SRT had a staff of 65 and attendances were running at 400,000 a year. It now has almost 250 staff and annual attendances of 700,000.
As a trustee Mr Irvine witnessed the opening of the South Mainland and Scalloway pools in 1993 and the Clickimin pool and bowls hall in 1995.
As chairman he presided over the opening of the Apex Fitness Centre at Clickimin in 2001; the West Mainland Leisure Centre in 2002; the extension of the North Mainland Pool in 2002; the replacement of the Clickimin running track in 2004; and the construction of the Clickimin squash courts in 2005.
Also in 2005, Mr Irvine was a key organiser when the NatWest Island Games were held in Shetland, including co-ordinating the sail boarding.
In 2013 he travelled to Brussels with the political leader of Shetland Islands Council, Gary Robinson, to receive the European Community of Sport Award on behalf of the trust.
He is currently chairman of the Voxter Trust which manages the Voxter Outdoor Centre and has served as a board member of NHS Shetland.