Brandon Bernard, 40, received a lethal injection in Indiana on Thursday after telling the couple he killed his was sorry.
Several high-profile figures, including reality TV star Kim Kardashian West, had appealed to Mr Trump to commute Mr Bernard's sentence to life in prison.
Before Mr Bernard's execution, Ms Kardashian West tweeted that she had spoken to him earlier: "Hardest call I've ever had.”
She added: “Brandon, selfless as always, was focused on his family and making sure they are ok. He told me not to cry because our fight isn't over."
He was convicted of murder in 1999 when he was a teenager, and is the youngest offender to be executed by the federal government in nearly 70 years.
It marks the ninth federal execution of the year, with four more federal executions, planned for the weeks before President-elect Joe Biden's inauguration.
The case of Mr Bernard was a rare execution of a person who was in his teens when his crime was committed.
Mr Bernard, 40, directed his last words to the family of the couple he killed.
"I'm sorry," he said, lifting his head and looking at the witness-room windows.
"That's the only words that I can say that completely capture how I feel now and how I felt that day."
Just before the execution was scheduled, Mr Bernard's lawyers filed papers with the Supreme Court seeking to halt the execution.
But about two and a half hours after the execution was scheduled, the Supreme Court denied the request, clearing the way for the execution to proceed.
#BrandonBernard should not be executed:
— Kim Kardashian West (@KimKardashian) December 10, 2020
1. He was 18 at the time.
2. He was not the shooter.
3. The prosecutor and 5 of the jurors now support clemency.
4. He’s spent decades in prison w/out a write up, helping at risk youth.
5. There’s bipartisan support for his commutation. pic.twitter.com/18GugdtuOs
