The Italian's future was in doubt after Friday's 6-1 World Cup qualifying defeat to Germany in Dublin.
However, the team bounced back from that humiliation with a 4-1 win in the Faroe Islands on Tuesday.
"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 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," read an FAI statement.
"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."
Ireland currently sit third in Group C with six points from their opening three matches.
Trapattoni took charge of the side in 2008 after an illustrious career in club management that included spells with AC Milan, Inter Milan, Juventus and Bayern Munich.