The 57-times-capped back row forward, follows in the footsteps of such rugby luminaries as Gareth Edwards, David Campese, Jonah Lomu, Martin Johnson and Jonny Wilkinson, in winning the Pat Marshall Memorial Award for season 2005-06.
The award was determined by a poll of rugby writers from the club's membership around the world and was presented tonight at the club's annual dinner.
It follows White winning the recognition of his peers as Players' Player of the Year in both Scotland and England last season during which he was also named Scotland Player of the Year.
White, who captained Scotland to victories over France, England and Italy, is currently on an extensive rehabilitation programme following surgery for a knee injury he sustained in the Test against Romania in November.
He said: "I'm obviously very pleased to win this award, particularly when I hear of some of the previous recipients. It's a bit frustrating at the moment being injured but I'm working hard on my rehab and hope to be back in action as soon as I can."
Scotland coach Frank Hadden said: "Jason thoroughly deserves this recognition. Not only has he received the plaudits of his peers but his contribution has been lauded by the rugby media too."