Robert Williams, 29, was high on cannabis at the time he drove at 100mph in order to avoid West Yorshire Police officers.
Leeds Crown Court heard Williams was forced off the road after he went the wrong way onto a roundabout and was about to drive onto the A64 York Road in the wrong carriageway.
The court was shown police dashcam footage of the three-and-a-half mile pursuit.
The incident began on the M621 slip road, off Cemetery Road, Holbeck, on October 17 last year.
Robert Galley, prosecuting, said Williams sped off in his VW Golf after officers indicated for him to pull over.
He went back onto the M621 and drove to the East End Park area of the city.
Footage showed Williams leaving the motorway and driving through a red light.
A pedestrian and other motorists had to take evasive action as he drove on the wrong side of the road.
A police car deliberately collided with Williams's vehicle as he tried to drive onto the A64 exit road.
Williams car span around before stopping and he was arrested.
He was found in possession of cannabis.
Tests later showed he had traces of the drug in his system above the legal level.
Williams, of Brignall Garth, Burmantofts, Leeds, pleaded guilty to dangerous driving, drug while under the influence of drugs, failing to stop and possession of cannabis.
The court heard Williams was on bail at the time of the offence awaiting sentence for conspiracy to supply cocaine and money laundering.
He was given a six-year sentence for those offences on December 22 last year.
Judge Simon Phillips, QC, jailed Williams for a further 12 months.
He ordered that the sentence run consecutively to the sentence he is currently serving.