Chadwick Banks, 43, was pronounced dead by lethal injection at 0027 GMT, said John Tupps, a spokesman for the governor of Florida.
The US Supreme Court had rejected his final appeal less than an hour before his death.
Banks was 23 when he was convicted of shooting his sleeping wife in the head and then raping the 10-year-old girl, before shooting her in the head too.
He was sentenced to life in prison for the 1992 murder of his wife and the death penalty for killing the little girl. He had confessed to both.
She said Banks was "the third person executed, all under (Florida) Governor Rick Scott, whose court-appointed, state-paid lawyer missed the federal court filing deadline so that his case has never been reviewed in federal court."
Banks was the eighth execution in Florida this year.
Eighteen US states have abolished the death penalty, but the 32 others -- and the federal government -- maintain the practice. Surveys indicate that it retains majority support among the US public.
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