Former Ireland defender McCarthy, 61, took over in November 2018 and was poised to lead them into last month's Euro 2020 qualifying playoffs before the coronavirus pandemic took hold.
Ex-Dundalk manager Kenny was due to replace McCarthy after the Euros but with the playoffs delayed and the tournament put back a year the FAI have brought the transition forward.
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"The Football Association of Ireland announces that Mick McCarthy is to be succeeded as national team manager by Stephen Kenny with immediate effect," a statement read.
"The handover has been agreed with both men in light of the delay to the European Championship play-offs caused by the COVID-19 pandemic."
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McCarthy's contract was due to expire on July 31, after the Euro 2020 finals that have now been re-scheduled for 2021.
"This move allows Stephen Kenny time to plan for the European Championship play-off semi-final against Slovakia later in the year," the statement said.
Kenny, 48, has been promoted from under-21s coach.
McCarthy's last match in charge was a 1-1 draw with Denmark in Dublin in November, meaning they missed automatic qualification for the Euros.
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