Lapasset told Press Association Sport's www.thesportbriefing.com that the IRB had agreed to support Argentina's initial introduction into the tournament with a one-off financial contribution of around USD 2 million.
The financial support is expected to be ratified by the IRB Council, removing the one remaining significant obstacle to Argentina joining the tournament, which includes South Africa, New Zealand and Australia.
"It is done," said Lapasset at the Global Sports Forum in Barcelona.
"The principle is to support the cost of the introduction of Argentina into the Tri Nations.
"It will be a one-off payment of around US Dollars 2 million. The principle is agreed, and we just need the IRB Council to confirm at the next meeting [scheduled for May 12].
"It will be done so Argentina can enter in 2012.
"We have an agreement with South Africa, New Zealand and Australia for the financial programme that is now in place, and the three existing nations are supportive."
Argentina's third-place finish at the 2007 Rugby World Cup highlighted the need for the team to engage in regular matches against top-quality opposition.
In September 2009, Sanzar, the board representing the national rugby unions of the existing Tri Nations teams, tabled a conditional invitation to Argentina to join the competition.
Aside from being geographically stranded on the global rugby map, the fact that most of Argentina's best players are based in Europe has also counted against bringing the South American country into the fold.
"The challenge now is to organise the travel arrangements between the countries," admitted Lapasset, who sits on the IRB Council.
"However, it is fantastic [that Argentina will join the Tri Nations].
"It started with the World Cup in 2007 and we realised the importance of creating a symbol in South America.
"It will help to build professionalism within Argentinian rugby."