Four men were arrested after the lorry knocked down and killed the pedestrian, who was in her 50s, hit two parked cars and smashed into the side of the house in Brierley, near Barnsley, South Yorkshire.
The incident, which happened at about 1.40pm on Friday, has been referred to the Independent Office for Police Conduct (IOPC).
South Yorkshire Police said the lorry had previously been reported as stolen.
A spokesman said: “It was travelling along Common Lane, towards Grimethorpe, when an officer in a marked patrol car, travelling in the opposite direction, turned around to follow the vehicle.
“The HGV then travelled on to Park View, where it was in collision with a pedestrian, a woman in her 50s.
“The vehicle then hit two parked cars before colliding with a house on the road and coming to a stop.”
The dead woman’s family has been informed.
The four arrested men were being held in custody.
The driver suffered minor injuries.
A large area remained cordoned off around the newly-built house, which has suffered severe damage at the back, with beds and other household items hanging precariously from the wrecked gable end.
People living close to the scene said they were alerted by a loud bang.
People who gathered to watch a large number of police, engineers and gas contractors working at the scene said police cars were there very quickly and men were seen leaving the cab of the tractor unit and running away.
They said no-one was in the semi-detached home, which had only been built in the last six months.
Some of the people who lived in the property returned shortly after the crash to find their new house wrecked.
One man, who did not want to be named, said: “It’s come and hit two cars and then just crashed right into the house.
“It hit the woman near the cars and it’s just terrible.
“The police were following it and it was obviously going too fast.”
Another man said: “I was standing outside that house earlier. I just can’t believe it.”
An IOPC spokesman said: “We were notified by South Yorkshire Police about this incident at around 3pm and sent our investigators to the scene and to the police post-incident procedure to gather information and assess the level, if any, of our future involvement.”
Anyone with information is asked to call 101.