Moeller, 60, was the second South Dakota inmate put to death in the last two weeks and died 22 minutes after receiving a lethal injection at the state prison in Sioux Falls.
KSFY-TV in Sioux Falls said Moeller told the prison warden he had no last words, then asked, "They're my fan club?" in apparent reference to the witnesses.
The execution brought an end to Moeller's 20-year stint on death row. He was sentenced in 1992 for the kidnapping and murder of Becky O'Connell two years earlier.
KSFY said Moeller abducted the child from a neighborhood within sight of the Sioux Falls prison where he was put to death.
Moeller spent much of his time in prison appealing his conviction. His appeals led to a new trial, but he was convicted again in 1997.
Moeller eventually conceded he had killed Becky and was prepared to pay the ultimate price.