Carney will resign on Tuesday at noon to begin the transition to his next post as mayor of Wilmington, Delaware.
That means Lieutenant Governor Bethany Hall-Long, who is next in line, will be sworn in as Delaware's 75th governor.
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Hall-Long will serve the remaining two weeks of Carney's term.
The position will then be taken up by Governor-elect Matt Meyer, who defeated Hall-Long in Delaware's primary election.