McCarthy, who managed the side from 1996-2002, will take over from Martin O'Neill who left the role along with his assistant Roy Keane on Wednesday after a run of six matches without victory.
McCarthy will manage the team until the end of their European Championship campaign and will then be replaced by Dundalk manager Kenny who has been appointed Ireland's Under-21 team manager.
McCarthy will hold his first news conference on Sunday, where he is expected to announce that long-term assistant Terry Connor and Ireland's record goal-scorer Robbie Keane will join his coaching staff.
The 59-year-old McCarthy led the country to the last 16 of the World Cup in 2002 and made 57 appearances for Ireland 1984-1992.
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The draw for the Euro Championship takes place in Dublin on Dec. 2.
(Reporting by Tom Hayward, editing by Ed Osmond)
