The 69-year-old, real name Royston Vasey, was filmed by a speed camera, reading while tailing a lorry in his white Lexus on the A19 in North Yorkshire.
Brown, who is from East Harsely, near Northallerton, was snapped heading south near Crathorne on May 15.
He did not appear at Northallerton Magistrates' Court yesterday but pleaded guilty by post to driving without due care and attention.
The wealthy comedian was fined £30 and received four penalty points on his licence. He also had to pay £40 costs and a victim surcharge of £40.
Dave Brown, North Yorkshire Police's mobile safety camera manager, said: "This is another case where our mobile safety cameras have proved that they are not just about speed, demonstrating that we have the technology to capture all manner of offences which put road users at risk.
"Motorists must give the road their full attention as a few seconds' lapse in concentration can have catastrophic consequences, literally meaning the difference between life and death."
North Yorkshire Post posted footage of Brown's bad driving online.