Martin O’Neill had been in charge since 2013, leading the country to the last 16 of Euro 2016.
He has now decided to stand down by mutual consent after a disappointing UEFA Nations League campaign which ended in relegation.
The national side has won only once in their last eleven games.
Assistant Roy Keane and O’Neill’s other backroom staff have also left their roles following Monday’s 0-0 draw with Denmark.
The Football Association of Ireland president Donal Conway said on the association’s official website: “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.”
FAI chief executive John Delaney added: “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.”