The stolen vehicles were used to plough into CCTV camera posts and bollards leading to a subway under the M1, before being driven across Temple Newsam Park Golf Course.
Police were alerted just before 10.50pm on April 23 when one of the dumper trucks was driven into a Leedswatch CCTV camera mounted on a post in Kendal Drive, Halton Moor.
The camera was knocked down and the front section of the vehicle overturned.
Two further cameras in the area were later found to have been damaged in the same way.
With support from the National Police Air Service helicopter, the second vehicle was found crashed and abandoned in woodland off Halton Moor Road.
Inspector Mick Preston, who heads neighbourhood policing in east Leeds, said: “The two vehicles that were stolen are very large earth moving machines and the way they were driven over some considerable distance could quite easily have resulted in someone being killed or seriously injured.
“As it is, the incident has caused many thousands of pounds worth of damage to council-operated CCTV cameras, to the golf course, to the two vehicles themselves and to other objects, such as fences, along the route they took.
“We are carrying out extensive enquiries to identify those responsible and are appealing for any information from the public that could assist the investigation."
Enquiries established that the two articulated dumper trucks had been stolen from a construction site in Knowsthorpe Lane.
It was found that they had been driven from the site onto Pontefract Lane through concrete bollards leading to a subway under the M1 and across the golf course, causing damage to the course itself.
Both vehicles were then driven through woods off Halton Moor Road where one vehicle was abandoned, before the other continued on to damage the CCTV cameras.
Forensic examination of both the dumper tracks has taken place.
Insp Preston said: "Witnesses have reported seeing a large number of people around the vehicle at the time it was used to damage the cameras and we are interested in speaking to any of those people.
“This has clearly been a deliberate attempt to disable the CCTV cameras which are there to deter and detect crime and assist in keeping people in that area safe.
“We know the law-abiding majority of people in the area will not condone this sort of behaviour and will support our efforts to find those responsible.
“We have put additional patrols in place to reassure the community while work is carried out to repair and replace the cameras.”
Anyone with information is asked to contact officers via 101, quoting crime reference 13180193455.
Alternatively, call the independent charity Crimestoppers anonymously on 0800 555 111.