Billy Hughes was found unconscious after apparently becoming entangled in the rope swing.
The tragic incident happened at his home in Balveny Street, Garthamlock at around 9.15pm yesterday.
A Police probe is now underway into the 10-year-old's "unexplained" death.
Police Scotland a post mortem examination is due to be held.
A spokeswoman said: "We received a report of a sudden death of a 10-year-old boy in his garden in Balveny Street in the Garthamlock area of Glasgow at around 9.40pm on Monday April 14.
"A post-mortem examination will take place in due course.
"At this time the death is being treated as unexplained.
"Inquiries are ongoing."