ITV Wales journalist Ian Lang reports
The pilot who suffered non-life-threatening injuries was airlifted to hospital from Bodffordd, near Llangefni on Saturday, 10 February.
Jeanette and Geoff Charley have lived in the house for almost 20 years, and say they were just settling down for a quiet afternoon when "all of a sudden" they heard "a great big bang."
"Before I could get up properly to go see what it was, the phone rang," said Jeanette.
It was her son, asking if they were okay because there had been a plane crash nearby.
Jeanette said she then went outside and asked a lady walking down the street if a plane had crashed in the street.
"Yes!" said the lady. "It's in your back garden!"
When she and her husband went outside to see for themselves, they were "totally floored" by a scene that was "surreal- like something out of a film!"
"There it was in all its glory, all mangled, stuck up by the trees in the back garden."
The couple feel incredibly lucky that the plane landed where it did - and not any closer to their house.
The pilot's injuries are non-life-threatening and North Wales Fire and Rescue Service say there were no other passengers on the flight.
While efforts to remove the wreckage begin, Jeanette and Geoff say it's just "absolutely amazing nothing more sinister" happened.