Andy Martin, London Irish CEO, said: "We've had to make a difficult decision to move our sell-out fixture against Leinster to Twickenham Stadium.
"However, we are delighted that more of our fans can now come and support us on what promises to be an excellent evening of top class rugby."
The switch from the Madejski Stadium to the home of English Rugby will increase the possible attendance for the potential Pool 6 decider and will be the third Heineken Cup pool match played at Twickenham Stadium, currently celebrating its centenary year.
When Harlequins played Munster at Twickenham Stadium in the 2004/05 tournament, they attracted a crowd of 33,883 and there were 33,282 at the ground when London Wasps met Leinster there last season.
And it will be the sixth tournament match staged at Twickenham Stadium following the Heineken Cup finals at the world famous ground in 2000, 2004 and 2007.
With a combined crowd figure for those three finals of 222,574, it means the London Irish v Leinster match later this month will see over 300,000 people having gone through the Twickenham Stadium turnstiles for six Heineken Cup matches.