Michael Tisius, 42, was convicted in 2001 of murdering Randolph County sheriff's deputies Jason Acton and Leon Egley, both unarmed, during a failed attempt to help a former cellmate escape from jail.
Tisius was pronounced dead at 6.10pm on Tuesday after he received a lethal injection as the US Supreme Court denied two petitions for a stay of execution on Monday and two more on Tuesday, the Missouri Department of Corrections said in a statement.
Lawyers for Tisius had argued in petitions seeking a reprieve that he should be spared the death penalty given he was 19 at the time of the killings and suffered from lifelong brain impairments and mental illness.
According to his lawyers, Tisius was traumatised by severe physical abuse and neglect as a child, aggravating cognitive deficits that rendered him vulnerable to manipulation by others, including his older cellmate, Roy Vance, who persuaded Tisius to go along with the ill-fated escape plan.
In his last statement, Tisius said he tried to become a better man and expressed his remorse.
"I am sorry," Tisius said.
"And not because I am at the end but because I truly am sorry."
Six former jurors among the 12 who voted unanimously to recommend the death penalty for Tisius at his trial in 2010 said in sworn affidavits as part of a separate clemency petition that they now favoured or would accept life imprisonment instead of capital punishment.
Governor Mike Parson, a Republican, declined the clemency bid on Monday.
"Missouri's judicial system provided Mr Tisius with due process and fair proceedings for his brutal murders of two Randolph County jail guards," the Republican governor said in a statement.
Tisius was accused of plotting with Tracie Bulington, Vance's then-girlfriend, to help Vance escape from jail after Tisius was released from the lockup.
He had met Vance while serving time for a probation violation stemming from a misdemeanour theft case, according to his lawyers.
The two guards were shot and killed when the breakout attempt went awry.
Bulington and Vance were later sentenced to life in prison for their roles in the incident.
