Olmstead joined Scottish in January, having previously played for Australian club Parramatta Two Blues and Calgary-based Prairie Wolf Pack.
The 25-year-old has won seven international caps for Canada.
"He will fit in well with the type of game we are trying to implement," said director of rugby Dean Richards.
"He is a typically hard Canadian player who brings a real no-nonsense edge to his play."
Premiership side Newcastle Falcons have signed Canada lock Evan Olmstead from Championship club London Scottish on a deal starting from next season.