Mick McCarthy returns as Republic manager
McCarthy, out of work since leaving Championship side Ipswich in April, has agreed a two-year contract to succeed Martin O'Neill.
McCarthy, whose first spell as Republic boss ended in 2002, has been tasked with securing qualification for Euro 2020.
"I'm honoured and excited to be back with the Republic of Ireland," McCarthy said.
"I am delighted that the FAI Board and CEO have given me this opportunity to lead the team to EURO 2020."
O'Neill and his assistant Roy Keane were sacked earlier this week after a disappointing run of one win in nine matches this year.
The FAI also confirmed Stephen Kenny's appointment as Under-21 coach, with the intention of him succeeding McCarthy after the 2020 finals.
McCarthy, who will be joined by his long-time assistant Terry Connor, has been out of a job since a poor run of form at Portman Road.
The 59-year-old added: "I have been involved in club football for the last 15 years, so this will be a new challenge but one that I know well.
"I'm delighted to have Terry Connor, a trusted colleague and excellent coach, and Robbie Keane, one of the finest players who I had the pleasure of managing, helping me as assistant coaches."
McCarthy won 57 caps for the Republic before taking charge of the country for the first time in 1996 after leaving his maiden managerial job at Millwall.
Under Barnsley-born McCarthy, the Republic missed out on qualification to the 1998 World Cup and Euro 2000.
His tenure concluded at the 2002 World Cup in Japan and South Korea, where, despite the departure from the squad of then-Manchester United star Keane following a bitter fallout with McCarthy, the Republic reached the last 16.
Since then, McCarthy has managed Sunderland, Wolverhampton Wanderers and Ipswich.
Aware of the irony that he returns to the Republic just as his old rival is departing, McCarthy insisted the Keane situation has long since been consigned to history.
Referring to the row, in which Keane launched a furious rant at McCarthy at the team's World Cup training base, McCarthy said: "I don't believe that my career or Roy's career should be defined by that.
"We both had successful playing careers - him far better than I - but then I've had a pretty successful career as a manager and I like to think I'd be remembered for that.
"I've got older and wiser and I've got a bit more perspective on life. I tend not to call out everyone as quickly as I did before.
"I'd like to think of the experience I've gained since I was here last time."