Dwain Francis, 35, was jailed for five years eight months at Stafford Crown Court after also admitting possession with intent to supply heroin and crack cocaine.
He was also disqualified from driving for four years 10 months.
The court heard that Francis, of Barnwood Road, Quinton, was driving his white BMW in Tamworth on January 21 when he failed to stop for officers.
He crashed into a red Corsa and white VW Golf, and then two police cars in Lud Lane and Ludgate.
An officer was taken to hospital with head and neck injuries following the crash. He had to be cut out of an unmarked police car by firefighters. He is now back at work on restricted duties and receiving physiotherapy.
Francis was sentenced for dangerous driving in Lud Lane and Ludgate on January 21, and possession with intent to supply heroin and crack cocaine.
Detective Inspector Tim Boulton, of Staffordshire Police, said: “This was reckless and dangerous driving in a bid to get away from officers and avoid discovery of the heroin and cocaine.
“Francis injured an officer who is still receiving treatment and could’ve seriously hurt members of the public. We’re glad he’s been sentenced for his actions.”