The New Zealand-born Scot, 27, made 76 appearances in six years with the United Rugby Championship winners.
"I've had a great time with Glasgow and enjoyed being part of a successful squad this season, but it's a good change and a big opportunity going to Newcastle," Gordon told Falcons' website.
"It's a new city for me, a new team and a new competition, so it's a real fresh start.
"I've already got a few mates down there who I know from my time in Scotland with the likes of Cammy Hutchison, Kiran McDonald, Murray McCallum and Cameron Neild. They're all good lads and I hear good things about the place so I'm excited to rip in."