The match had been scheduled to take place at Wasps' usual home of Adams Park in Wycombe but has been moved to the headquarters of English rugby to accommodate a bigger crowd.
"Taking a Heineken Cup game to the home of English rugby is fitting, especially as we face one of the strongest sides in Ireland," said McGeechan, who leads the Lions to South Africa in eight months time.
"We've enjoyed great displays there and the support has been overwhelming.
"The supporters will make this game the spectacle that it can truly be and I hope that many of them will get behind the team and look to another big game."
Adams Park has a capacity of 10,000 and, with a crowd of 8,800 in attendance last Sunday to see Wasps beat Castres 25-11, chief executive Tony Copsey believes that demand would have outstripped supply for the clash with Brian O'Driscoll and co.
"This gives us another opportunity to welcome a larger crowd to a big Wasps occasion," said Copsey.
"The support and interest in the European competition shows us that a game of such standing - between the reigning champions of England and Ireland, is deserved of a place on one of the world's greatest rugby stages.
"It is our intention to open the lower bowl of Twickenham, holding a capacity of 30,000.This gives our players and supporters an opportunity to make this one of our biggest fixtures of the season."