Cleveland Police said the incident occurred at 3.39am on Saturday near the South Bank area east of Middlesbrough and that all occupants of the two vehicles died at the scene.
A Volkswagen Passat was travelling the wrong way down the A66 and collided head-on with a police vehicle on the same road, police said.
"This is an incredibly sad day for Cleveland," Cleveland Police Chief Constable Victoria Fuller said.
Fuller named the two dead officers as police constables Matthew Blades, 37, and Tom Clough, 38, describing them as "brave officers ... who didn't return home to their families at the end of their shift".
Prime Minister Andy Burnham also released a brief statement expressing his sadness at the incident, which as usual in such cases will be reviewed by the United Kingdom's Independent Office for Police Conduct.
A large white tent was erected over the scene on Saturday, with multiple emergency service vehicles around.
Police have put into effect a drone exclusion zone around the site of the collision.
Local councillors David Taylor and Stephen Martin said in a Facebook post they were "deeply saddened" by the "unimaginable tragedy".
Following two recent head-on crashes near Dublin, one of which killed five people, Ireland's police chief this week warned that some young people were driving the wrong way on the motorway "for social media likes".
An Irish parliament committee has asked short-form video platform TikTok to explain how it removes content "that appears to glorify dangerous and illegal behaviour on our roads".
On Tuesday, Ireland's media regulator made a similar request.
with PA
