McCarthy, the former Ireland captain who managed the side from 1996-2002, takes over from Martin O'Neill who left along with assistant Roy Keane last week amid a run of six matches without victory and ahead of qualification for the Euro 2020 finals when Dublin will host four games.
In an unusual move, McCarthy will manage the team until the end of that campaign and then be replaced by Kenny, who has led Dundalk to four League of Ireland titles in five years and will become Ireland's Under-21 team manager in the meantime.
McCarthy took Ireland to the last 16 of the 2002 World Cup, although the build-up to the tournament was marred by a public row in Saipan with then Ireland captain Keane, who walked out on the team. McCarthy resigned later that year.
"I'm honoured and excited to be back with the Republic of Ireland. I am delighted that the FAI Board and CEO have given me this opportunity to lead the team to EURO 2020," McCarthy said in a statement.
"I am looking forward to getting started and embracing this challenge to qualify for EURO 2020, where it would be fantastic to play in front of the Ireland supporters in Aviva Stadium." (Reporting by Padraic Halpin and Conor Humphries Editing by Toby Davis)
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