Gray, 20, who has won two full Scotland caps this season, received the Sir Willie Purves Quaich at a gala dinner at the Caledonian Club in London earlier this week.
Edinburgh flanker David Denton and Scotland and British & Irish Lions lock Richie Gray - Jonny’s older brother - are among previous recipients of the award.
Previous recipients of the award have included David Denton and Jonny’s older brother, Richie.
Gray said: “I’m very honoured to have received this award and I thank the Friends of Scottish Rugby for considering me worthy of it.
“My focus now is on a really big end to the season, starting with Glasgow Warriors’ game against Treviso tonight.”
Scotland under-20 back-row forward Tommy Spinks received the Sir Tommy Macpherson Quaich as the young London Scottish Player of the Year.