The Monty Python stage show has been extended from one date to five, running from 1 to 5 July at London's O2 Arena.
The first show sold out within 43.5 seconds, organisers announced.
The other four shows then sold out within 55 minutes. There were 14,500 tickets up for grabs for each show.
Eric Idle said: "It's totally amazing. I don't think we realised quite how much Python is loved round the world. We look forward to paying off Terry Jones' mortgage soon."
Last week it was announced that John Cleese, Terry Gilliam, Michael Palin, Terry Jones and Idle were to reunite and perform together.
It will be the first time the anarchic comedians have performed together since 2009, at their 40th anniversary celebrations in New York.
However, several readers of the BBC News website stated that despite trying to buy tickets for the show announced last week, they were unable to, as many had been sold to "ticket marketplace" websites, which buy and sell live event tickets.
One reader said: "Within minutes of tickets going on sale (and 'selling out')" many marketplace websites "had thousands of tickets for sale at ridiculously inflated prices".
They added that that it was "one of the worst examples of rip-off Britain".
One marketplace website, viagogo, had Monty Python tickets for Saturday 5 July listed as ranging from £136.88 to £3,999 [at the time of writing].
Viagogo said in response to the BBC readers' comments: "Every now and again, a show will be so popular it sends ticket prices rocketing.
"This is one of those times, with demand for Monty Python's shows so high it is even outstripping demand for the Rolling Stones' 50th Anniversary concerts, with Viagogo recording over 30% more searches for the Monty Python shows than that seen in the same period for the Stones in 2012."
Published: 26/11/2013 09:04:09