Tickets for the 22 dates at London’s Hammersmith Apollo went on sale at 09:30 GMT on Friday morning.
Kate Bush, 55, said she was “completely overwhelmed by the response”.
“Thank you so much to everyone,” the singer added.
The Before the Dawn concerts, which take place this August and September, mark Kate Bush’s first return to the stage since The Tour Of Life in 1979.
Demand was so high that Kate Bush’s own website, as well as some ticket-selling sites, crashed as people tried to log on.
Tickets with a face value of £135 ($215) were already being offered on sale on secondary ticketing sites for more than £1000 ($1,500).
Kate Bush was just 20 when she completed her one and only tour, a year after topping the charts with Wuthering Heights.
The six-week tour, which travelled around Britain and mainland Europe, ended at the Hammersmith Odeon – now the Hammersmith Apollo.
Following the initial announcement of 15 dates last week, seven more dates were added in response to “massive pre-sale demand”.
Kate Bush, whose hits include Running Up That Hill and Babooshka, last released an album in 2011 – 50 Words For Snow.
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