Her speech Friday effectively puts a stop to the contest. The final result had been in doubt for 10 days after the election.
Abrams says she'll file a federal lawsuit to challenge 'gross mismanagement' of Georgia elections.
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Abrams made her announcement just after 5 p.m. That was the earliest state officials could certify the results after a court-ordered review of absentee, provisional and other uncounted ballots. Abrams' campaign had contended there were potentially enough uncounted votes to force a runoff.
Abrams had hoped to become the first black governor of the Deep South state and the first black female governor of any state.
Kemp is Georgia's former secretary of state. He was backed by President Donald Trump.
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Abrams stressed as she spoke: "This is not a speech of concession."
A spokesman for the Kemp campaign didn't answer his phone and didn't immediately respond to a text message seeking comment after Abrams' speech.