The incident happened just after 8am on Tuesday as officers chased the animal through the Inveralmond Industrial Estate area.
It had been on its way to slaughter at a nearby abattoir when it broke out.
A local resident filmed the slow pursuit by a police car and a police van as the bull trotted along Bute Drive.
Perth Grammar School gates were closed to vehicles and pupils were directed into the building when the bull was on the loose.
A spokesperson for Perth and Kinross Council reported: “The school was alerted to the escaped bull at 8.40am by Police Scotland.
“To ensure the safety of pupils, parents and staff the school gates were closed to vehicles and all pupils were immediately directed into the building.”
It was reportedly contained in a fenced area near to Perth Grammar School and nearby roads were closed.
Soon after 10am, a shot was heard by North Muirton residents after a marksman was called in to destroy the animal after it became a danger to the public.
A Police Scotland spokesperson said: “We were made aware of a loose bull in the area of the Inveralmond Industrial Estate in Perth shortly after 08.10am on Tuesday, 26 October.
“Unfortunately the animal continued into a residential area where it was safely contained by officers.
“All efforts were made to recover the bull but sadly the animal had to be destroyed at the scene.”