Martin O'Neill has stated that he left his role as Republic of Ireland manager "with a heavy heart", having fulfilled one of his "lifetime ambitions" by taking on the role.
His five-year tenure as Republic boss ended on Wednesday after Ireland failed to win a game as they were relegated from Nations League Group B.
The Football Association of Ireland said O'Neill's departure, and that of Roy Keane as his assistant, was by mutual consent, adding that its board "will meet promptly to discuss the process of recruiting a new manager".
In a statement released by the League Managers' Association, O'Neill said: "I have had the great honour of managing the Republic of Ireland national football team for the past five years and it is with a heavy heart that I leave this role.
"It was one of my lifetime ambitions to take charge of the Irish senior squad and I would like to thank the FAI board for giving me that opportunity.
"I will not forget the night in Lille when we beat Italy to secure the nation's best-ever achievement in the Euros competition, the terrific night we beat the world champions Germany at home in Dublin, or James McClean's goal in that euphoric win against Wales in Cardiff that put us through to the play-offs for this year's World Cup.
"The Irish fans have been a source of motivation to myself, the team and the whole backroom staff, embodying the passionate Irish spirit, and I thank them for their fervent support of the team.
"I am also very proud of the relationships I have built with the players, who have carried that very same spirit, imbued by the fans, on to the field of play."
O'Neill added: "A special thanks to Roy Keane my assistant, an inspirational figure in the world of football, Seamus McDonagh, Steve Guppy and Steve Walford for their brilliant contributions and to those backroom staff at the FAI that were of enormous help to me.
"Knowing that the past year would be a transitional phase for the squad, I have capped 12 new players in the last nine games, with the aim that they become significant international contributors in the coming campaign.
"To the players, I reserve great praise and admiration for the phenomenal commitment they have shown whilst wearing the Irish shirt. Having had these great experiences in my spell as the Irish international manager, I am looking forward to my next adventure in football."