The attorneys for Collings had argued that the police chief, who obtained their client’s confession and was the primary witness at his trial, had a troubled history and lacked credibility.
In addition, they said, the girl’s stepfather, David Spears, confessed to involvement in her death but did not face murder charges.
Missouri Governor Mike Parson denied a clemency request from Collings, clearing the way for his execution by lethal injection.
“Mr Collings has received every protection afforded by the Missouri and United States Constitutions, and Mr Collings’ conviction and sentence remain for his horrendous and callous crime,” Parson said.
“There is not and never has been any doubt about Collings’ involvement or the heinousness of his crimes.”
There have been 23 executions in the United States this year, including four in Missouri.
The death penalty has been abolished in 23 of the 50 US states, while six others - Arizona, California, Ohio, Oregon, Pennsylvania and Tennessee - have moratoriums in place.