Tickets for the three shows at the SSE Hydro on Saturday, January 18 and Sunday, January 19 were snapped up by petrolheads when they went on sale at 9am today.
Organisers have now confirmed that a fourth show will take place at the Hydro on Sunday, January 19 in a bid to meet the exceptional demand.
More than 12,000 people registered to pre-order some of the 24,000 tickets available for the first three 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.
Clarkson said: "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."