His family made an emotional appeal for information after he was reported missing on Monday.
But he has now been found safe and well near Milngavie, Police Scotland confirmed tonight.
He is currently understood to be receiving hospital treatment.
Jamie's disappearance had been widely followed by social media users around the Glasgow area.
Yesterday, we told how his grandmother, Geraldine McAllister, 61, was desperate for news of 19-year-old Jamie.
Making a direct plea to Jamie, the grandmother-of-10, said: "Please just get in touch, Jamie.
"If there is anything worrying you, it's not a problem. I just need you to get in touch, a phone call, a text message, anything."
Jamie, who is originally from Knightswood in Glasgow, was last seen at his flat in Rowan Road, in Cumbernauld on Monday afternoon.
He sent a text message to his friend at around 3am the same day, and that was the last time his mobile phone was used.
Mrs McAllister, a pub manager from Airdrie, had told the Evening Times: "We are going through hell, it's a nightmare. I'm just numb and I can't even bring myself to think about where Jamie might be.
"We don't know what the text said, but his friend said Jamie sounded vulnerable. That's not the Jamie we know. We're a really close family and he has never said anything was wrong.You read about this happening to other families, but you never think it's going to happen to you."
The former Knightswood Secondary pupil had recently decided he wanted to go to college to study Business Management.
His family describe him as a "polite, well-mannered, and sociable young man."
Jamie's dad Steven, who is in the Navy, had travelled back to Scotland from Plymouth to search for his son.