Tickets for three 90 minute shows at the arena were snapped up by petrolhead when they went on sale last Friday, causing organisers to add a fourth date to cope with demand.
A fifth show on Friday, January 17 has now also been added. Limited tickets are still available for the four previously announced shows, which will take place at 3.30pm and 7.30pm on Saturday, January 18 and 2pm and 5.30pm on Sunday, January 19.
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.
Hammond said: "Good news. Due to the phenomenal demand we're releasing another date."
Organisers have confirmed that the fifth performance will be the final date announced for the show.
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."