The game, between representative sides from the northern and southern hemispheres, has been arranged by the International Rugby Board and will be played on March 5.
RFU chief executive Francis Baron said: "On behalf of the RFU we are honoured to have been asked by the IRB to host this unique game for such a worthwhile cause.
"Everyone was touched by the tragic events in the Indian Ocean and its essential that as much money as possible is raised to help the relief effort.
"Our aim is to deliver Â£3million to Â£4million to the fund by providing the stadium free of charge and donating all the match-day profits from ticket sales, TV rights, sponsorship, hospitality, bar and rugby store to the fund."
Howard Thomas, Chief Executive of Premier Rugby Ltd, said: 'Premier Rugby will be providing the players required from England for the game and we're delighted that we can help such a worthwhile cause.
"I would encourage all sports fans to buy a ticket. By doing so they will be helping to raise vital revenue for the victims of the Tsunami.'