The 73-year-old Italian keeps his position despite a testing period for the Boys in Green, including their worst ever performance at the European Championships and a record defeat
The Italian's future was under review at an Extraordinary General Meeting of the governing body's board of directors in Dublin on Wednesday evening following a difficult period for the Boys in Green.
Ireland's 6-1 defeat by Germany on Friday was their worst ever in a competitive home game and made up four of five losses in the team's five most recent competitive matches before Tuesday's 4-1 win over Faroe Islands.
Trapattoni has also fallen out with squad members including James McClean, Stephen Kelly and Darron Gibson since leading his side to the worst ever performance by any country at a European Championship in Poland and Ukraine during the summer.
A statement from the FAI on Wednesday read: "The board of the FAI met today and discussed Ireland's performances in the World Cup qualifying campaign to date and the prospects of achieving qualification for Brazil 2014.
"The board agreed that convening a meeting between the Germany and Faroe Islands matches and/or commenting on the Germany game or the manager's position prior to [Tuesday's] game would have been totally inappropriate.
"Following today's discussions the board, while disappointed like everyone with the poor result and performance against Germany and understanding the frustration of some of our supporters, believes that the current position in the group means that qualification for Brazil in 2014 remains a realistic and achievable prospect and reaffirmed that Giovanni Trapattoni is to remain in charge of the national team.
"The board recognises the depth of feeling surrounding the team, the performances, the results and the manager, reflecting the passion which everyone in Irish football has for the game and will continue to work closely with the manager."