Ms Osborne was struck in Stowe Road, Langtoft at about 7.20am. She was taken to Peterborough District Hospital but sadly died later.
The ambulance had been on its way to a car accident in Stowe Road when it skidded on ice, overturned and hit the woman. The ambulance ended up on its roof in a ditch alongside the road.
A loud bang and deafening sirens were heard by nearby residents who ran to help.
Two paramedics in the ambulance were treated in hospital for minor injuries and both are said to be in a state of shock. The male driver was able to clamber out of the vehicle but his female colleague had to be freed by the fire service.
Police have now launched an investigation into the crash and are appealing for witnesses while East Midlands Ambulance Service has sent its sympathies to the woman's family.
The partner of the woman was comforted by police officers and family members as he paid a visit to the scene of the accident.
The road was closed until about 1.30pm while work was carried out to recover the ambulance.
Steve Thomas, 49, of Stowe Road, Langtoft, said: "We have seen two cars career off the road and one lady killed today, what else will it take for the authorities to listen to us and get these roads gritted.
"The death of this lady is a terrible tragedy."
One resident who didn't wish to be named said: "A number of local residents heard a bang and went out to the scene.
"The male driver of the ambulance had managed to free himself but the female crew member was trapped in the vehicle until the fire service arrived.
"Residents also attended to the pedestrian who had been hit, keeping her warm and reassuring her until an additional ambulance arrived."
As the schools finished for the day yesterday, pupils from Langtoft Primary School could be seen gathering around the ditch to talk about what happened.
The partner of the woman, who has not been named by police, was comforted by police officers and family members as he paid a visit to the scene of the accident.
A spokesman for East Midlands Ambulance Service said: "An ambulance responding to a 999 call with blue lights and sirens overturned and collided with a pedestrian.
"The pedestrian and both crew members were transported to Peterborough District Hospital for treatment. Tragically, the pedestrian has since passed away and we offer family and friends our deepest sympathies.
"The crew have suffered shock and are being treated for minor injuries. We are working with the police to assist them with their investigation."
Anyone who witnessed the accident is asked to call police on 01522 558855.