The 24-year-old, who was called up to the Scotland squad for the first time during the autumn internationals, is the joint-top try scorer for the Warriors this season.
The US-born back has registered five tries this campaign, with all of them coming in the RaboDirect PRO12, where Glasgow currently sit fifth in the table.
"I said when I joined Glasgow that it was a little like coming home because of the family connection and I'm really settled here," said Seymour.
"The way the squad and team are developing is a massive factor in staying on because the players and coaches here do believe that we're building towards something special.
"It's an exciting place to be at the moment and even though the results don't always go your way, we know we're headed in the right direction."
Seymour was raised in Nashville, Tennessee before moving to Northern Ireland via a spell in Dubai. He spent a season with Ulster before moving across the Irish Sea in 2011.
With Glasgow hosting Edinburgh in a crunch derby on Friday, Seymour is hoping to be back among the tries as they attempt to end a four-game losing streak.
"The game against Edinburgh at Scotstoun is massive for us as a club, not just because of the intensity of the rivalry, but for our season and for our position in the league it's vital we do everything we can to pick up points," he said. "I came here to play regular rugby and to get that call-up to the Scotland squad was a real vindication of the hard work, though I know, given the talent that is now in the Warriors squad, that I have to keep at it and keep trying to get better."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.