The 72-year-old Italian ended Ireland's 10-year wait to reach a major tournament when he guided them to the Euro 2012 finals earlier this month with a 5-1 aggregate play-off victory over Estonia.
"He's achieved, it's as simple as that," FAI Chief Executive John Delaney told state broadcaster RTE. "It's right and proper that he should manage us for the next two years."
After taking over the Ireland job in 2008, his contract had been due to expire at the end of the European Championships campaign. Assistants Marco Tardelli and Fausto Rossi have also agreed to contract extensions.
"It is a huge honour and a privilege," Trapattoni said in a statement.
Trapattoni said he had no fear of Europe's big names when the draw is made for the Euro 2012 finals, co-hosted by Poland and Ukraine, on Friday. But he said he would rather avoid his native Italy, who he managed from 2000-2004.
"With our mentality we can do well," he told Newstalk radio.
Delaney declined to say what the FAI would pay Trapattoni, but said he had agreed to take a pay cut to take account of Ireland's economic problems.
"They are very much aware of how difficult things are in Ireland," Delaney said.
Irish media reported that Trapattoni would be paid 1.5 million euros per year, down from 1.8 million euros. The FAI confirmed businessman Denis O'Brien would again subsidise the cost.
High pay for public officials is hugely sensitive in Ireland, which is recovering from a deep recession after the bursting of a huge property bubble, but Trapattoni enjoys overwhelming popularity from the Irish public.
Ireland's last appearance at a major championship was at the 2002 World Cup co-hosted by Japan and South Korea.
