More than one million people registered for the gig online after being told that tickets were available to buy.
Ticketmaster boss Chris Edmonds said: "It was a dramatic moment - the sales went live and there was a huge surge as fans bombarded the lines."
The reformed girl band will take to the stage at the O2 Arena in London on December 15. Tickets for two further dates - December 16 and 18 - are being sold to fans who originally registered in June.
A fourth concert in the capital, to be held on January 2 next year, is also listed on Ticketmaster's website.
The band's world tour begins in Canada on December 2.