The former Celtic boss had been in charge of the country for five years, leading them to Euro 2016, but they earned just two points in Nations League Group B3, scoring a single goal in the process.
O'Neill has, therefore, elected to leave the post.
In a statement, the FAI confirmed that Roy Keane, Seamus McDonagh and Steve Guppy have also departed.
The association praised the manager's contribution, stating: "O’Neill oversaw 55 games for Ireland during a five-year period and enjoyed unforgettable wins over World Champions Germany, Bosnia & Herzegovina, Italy, Austria and Wales.
"He ran the best EUROs campaign in Ireland's history and followed that by making it out of a tough group to reach the play-offs for the 2018 FIFA World Cup.
"He used 65 players in that time, giving 28 of them their first senior caps."
FAI President Donal Conway said: “On behalf of the FAI Board, I would like to thank Martin, Roy, and the management team for their work with the Republic of Ireland team over the last five years.
“Martin ensured that we enjoyed some great nights in the Aviva Stadium and on the road in Lille, Vienna, and Cardiff, which were fantastic high points for Irish football.”
FAI Chief Executive John Delaney echoed those sentiments: “I would like to thank Martin, Roy, and the management team for the impact that they had with the Ireland team. There have been many highlights during Martin’s reign – none more so than EURO 2016 in France, which will live long in the memory of all Irish supporters.
“Martin did a great job guiding the team out of a difficult qualifying group – where we beat World Champions Germany along the way – to reach EURO 2016 and advance to the Last-16 following a historic victory over Italy in Lille.
“I wish Martin, and the management team, the very best for the future.”
The FAI has confirmed that it will meet to discuss appointing a successor to the 66-year-old, who has also had spells in charge of the likes of Leicester, Aston Villa and Sunderland.