After an initial four-year spell at Scotstoun, Vernon, 30, rejoined Warriors in 2013 after two seasons with Sale Sharks.
He played a key role in Glasgow's PRO12 title success in 2015, starting the 31-13 final victory over Munster.
"I'm really excited to join London Scottish" Vernon said.
"I enjoyed hearing the vision that the management have for the club and was immediately convinced it was the right move. This unique opportunity was too good to pass up."
Vernon achieved the rare feat of representing an international team as both a forward and a back, playing for Scotland as a back-rower and a centre as he amassed 25 caps.
His career has been blighted by serious injury in recent times. He had a 14-month lay-off after struggling to overcome a shoulder problem, and then another 10-month absence after requiring Achilles surgery.
Vernon plans to combine his rugby duties at London Scottish with preparations for a career in finance when he hangs up his boots.
Glasgow Warriors head coach, Dave Rennie, said: "Richie is an incredibly good man and has contributed a hell of a lot to the club over a number of years. We wish him well transitioning into life after rugby with London Scottish."