It is expected that the group will announce a third concert for the Sunday night.
Tickets for the two shows on July 24 and 25 will go on sale next Friday March 20 at 8am priced from €33.80 and are expected to be snapped up.
The extravagant 'U2360' tour will journey to 14 European cities before moving onto America, Canada and South America.
The gig features a specially designed in-the-round set which will be placed at the centre of the pitch in Croke Park. A futuristic canopy covers the stage and a wrap-around screen will portray large images of the rockers to the audience. The aim is to achieve best views for all fans in the massive stadium.
Their new album, No Line on the Horizon, made its debut at the top of the US charts, the seventh number one success for the band.
The album is heading for the top slot in 30 countries worldwide this weekend having made its debut at number one in the UK charts. A total of 484,000 copies were sold in its first week.
This week the band played an intimate gig for 950 lucky US fans in Somerville, Massachusetts, where they revealed they would like to re-record some of their earlier material including the 1980 album Boy.
"The early records, there's [sic] some beautiful songs that feel a little bit unfinished to us," Bono commented.
Band manager Paul McGuinness said that U2's 360 tour is one of their most ambitious.
"U2 has always been at their best when surrounded by the audience, this staging takes a giant leap forward," said Mr McGuinness. "We have worked very hard to ensure U2 fans can purchase a great priced ticket with a guaranteed great view."
And promoters have revealed that the special guests for the two gigs in Dublin would be Glasvegas and the Kaiser Chiefs.
Thousands logged on to U2.com to obtain information about the upcoming tour when it was launched last week, causing the website to crash.
Demand for tickets for the show is expected to be massive, with tickets limited to six per person, purchased through Ticketmaster.