Letters found at Speed's home also said she would "rather that Archie be dead than see him leave with his father".
A jury of ten women and two men took five-and-a-half hours to find Speed guilty by unanimous verdict following a two-week trial at Birmingham Crown Court.
Speed, who wore a grey cardigan and jogging bottoms, burst into tears when the verdict was read out and shouted: "No, no, you've got it wrong.
"My kids are my life, they are my world. Nothing would make me take their life, my kids are my world.
"You're wrong, you're wrong. Nothing would ever make me take him out of this world. It's wrong. You're wrong."
The court heard the charity worker flipped when she became worried that Spriggs would take Archie to live with him and his new wife in Slovakia.
Speed's new partner, who found Archie's lifeless body, said she was stressed and had sent a string of disturbing text messages before the murder.
One message said: "I don't want to be in this f***** up world."
Another text mentioned her son: "I really don't want to be here. I wish we could just go to the coast and never come back or die so I don't have to feel like this again.
"I feel like I am losing it and I have an overwhelming feeling I am going to lose Archie."
The court heard Jones' conversation with the ambulance service holder and he said: "There's blood everywhere. She's cut herself.
"Her son, he's dead. He's freezing cold. He's blue. I think he's been smothered.
"She found him hanging from his scarf. She dragged him on the bed and smothered him.
"I'm shocked. It was the last thing I was expecting when I came home from work."
In the call, Jones claimed that Speed was "stressing out" about the forthcoming custody hearing.
Jurors also heard that Archie was known to social services and had been the subject of an Early Health assessment in the months before his death.
Just one week before the murder, teachers at Rushbury Church of England School in Church Stretton, alerted social services after becoming alarmed at Speed's state of mind.
The court heard how Speed had been diagnosed with depression in 1998 and 2014.
Speed always denied murdering Archie and claimed she found his body hanging from his bunk bed but forensics revealed he had probably been strangled and smothered.
Justice Nicol, adjourning proceedings, said he would sentence Speed on Tuesday.