He was in a Ford Focus which was followed by officers through Sheffield and along the Sheffield Parkway.
The car was abandoned after it crashed into a bollard, damaging the front passenger side wheel.
South Yorkshire Police said the driver and his passenger both jumped out of the car and fled, but were tracked down by a police dog and arrested by officers.
The car they were in had been stolen from Humberside last year.
A South Yorkshire Police spokesman said: "One of our patrols saw a Ford Focus last night on Sheffield ring road. It was quite happy being followed by one of our marked cars until it reached Park Square roundabout when it started to make off from us, heading generally towards the Manor.
"The pursuit was quite short, lasting only a minute or so, before the driver of the Focus managed to collide with a sneaky concrete bollard, causing enough damage to the front passenger side wheel that they couldn’t continue to drive any further.
"The two people in the Focus decided to try to continue the chase by running from the vehicle. This was a mistake.
"Following just behind the pursuing police vehicle was one of our dog handlers, bringing with him Police Dog Digby.
"Once Digby was out of the car, it wasn’t long before the two people that ran from the Focus were wearing bracelets and on their way to the cells.
"The Focus turned out to be a stolen car, stolen in a commercial burglary in the Humberside Police area last summer. Both driver and passenger were shipped off to speak to our Humberside colleagues this morning."