The driver drove at speeds of more than 100 miles per hour on the M1 northbound when he was clocked by Derbyshire Roads Policing Unit.
The man then "drove erratically" before being boxed in by officers from Derbyshire and South Yorkshire near Sheffield.
Both forces described the operation as great "teamwork".
A spokesman for Derbyshire RPU said: "Another lovely piece of teamwork. Driver zooms by us, then weaving from lane to lane at 110mph.
"Boxed in and driver says he never even saw us. Drugged up.
"South Yorkshire Police custody facilities used and blood obtained."
A spokesman for South Yorkshire Police added: "Great teamwork between ourselves and Derbyshire RPU.
"Driver passes one of their marked traffic cars at over 100 mph and drives erratically on M1 Northbound.
"We provide a welcome to South Yorkshire.
"Vehicle boxed in, driver arrested for drink and drug driving by Derbyshire."