The 43-year-old from Collingham in the English county was charged in August and will now appear at Nottingham magistrates' court later this week.
The service stated that the charge relates to a video file that was recovered by police back in February, and it is deemed to be a Category A file, the most serious in this case.
Coote was sacked by PGMOL back in December 2024, following a video that surfaced allegedly showing the former referee making offensive comments about the then Liverpool manager, Jurgen Klopp.
He was also banned until June 30th 2026 by UEFA after another video showed him snorting a white powder whilst in Germany at EURO 204.
Coote has been conditionally bailed.