The 74-year-old Italian, who had been in charge for over five years and steered Ireland to the Euro 2012 championship, left by mutual consent, the Football Association of Ireland said.
Ireland had been in contention to claim a playoff spot for next year's World cup in Brazil but defeats in their last two Group C games has left them in fourth spot with two games left.
"We thank Giovanni Trapattoni, Marco Tardelli and Franco Rossi for the last five and a half years during which we qualified for our first major tournament in 10 years and were close to qualification for 2010 World Cup in South Africa after the play-off in France," FAI Chief Executive John Delaney said in a statement.
"This particular World Cup campaign has been disappointing but Giovanni leaves us with a group of good young players which should form the basis of the squad that the new manager will use for the European Championship in France 2016 when 24 teams qualify."
Former Milan player Trapattoni was one of Ireland's highest-profile managers, having been in charge at some of Europe's biggest club sides including Juventus, Inter Milan and Bayern Munich as well as the Italian national side.
Trapattoni said he believed he had left Ireland in good shape for the challenges ahead.
"I would also want to thank all FAI staff members, including the backroom team and the players who have been great to work with during the last three campaigns," he said.
"I wish them well in the future and hope that the job we have done leaves everything in a good place for my successor to take over."
- Sports & Recreation
- Giovanni Trapattoni
- Marco Tardelli