The SSE Hydro will host three Top Gear Live shows on January 18 and 19 2014.
More than 12,000 people have already registered to pre-order some of the 24,000 tickets available for the action-packed shows.
The 90 minute performances will be presented by Jeremy Clarkson, James May and Richard Hammond and will include stunts, supercars, dramatic challenges and the Stig.
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Clarkson said: "People of Scotland, we have good news. Our ambitious arena show which is known all over the world is coming north of the border for the very first time. We will see you there... unless you've got anything better to do!
"I've absolutely no idea exactly what we'll be up to in Glasgow but, as this is the first time we've ever performed live north of the border, you can guarantee it will be something very special. What we can promise is lots of gigantic explosions, some very scary stunts plus a magnificent line-up of incredibly expensive supercars... not to mention all the usual cock-ups, crashes and arguments. Who knows, you might even see The Stig in a kilt."
The show has been on a world tour for the last 12 months, visiting Moscow, Sydney, Amsterdam, Antwerp, Durban and Poland. The Glasgow shows will be the first time the Top Gear team has performed in the UK since their headlining show at the Birmingham NEC in October 2012.
Clarkson added: "I'm told the building [the Hydro] was inspired by ancient Roman and Greek amphitheatres so it sounds like the perfect setting for our kind of arcane humour and barbaric acts. I think some epic chariot racing should be on the cards!"
Tickets for the shows officially go on sale at 9am tomorrow (Friday).
For more information visit the Top Gear Live website.