Nottinghamshire Police say the charge relates to a video file recovered by police officers in February 2025.
Coote, 43, will appear at Nottingham Magistrates' Court on Thursday, September 11.
The former match official was charged on August 12 following an investigation by Nottinghamshire Police and has been on conditional bail since.
Coote has not officiated since he was suspended by the Professional Game Match Officials Limited (PGMOL) on November 11 after a video emerged on social media of him calling former Liverpool manager Jurgen Klopp "f***ing arrogant" and a "German c***".
On November 14, The Sun published a separate video which it claimed showed Coote sniffing white powder through a rolled-up American bank note. The Sun said the video was from July 6, the day after the Euro 2024 quarter-final between France and Portugal in Hamburg where Coote was the assistant VAR.
Coote's contract with PGMOL was terminated on December 9. In February he was banned from officiating in UEFA competitions for 16 months for "violating the basic rules of decent conduct" and "bringing the sport of football, and UEFA in particular, into disrepute".
In August, he was given an eight-week suspension by the Football Association following his comments about Klopp.
In an interview with The Sun on January 27, Coote came out as gay and said that the effects of hiding his sexuality contributed to the behaviour that led to his dismissal.
"My sexuality isn't the only reason that led me to be in that position," said Coote. "But I'm not telling an authentic story if I don't say that I'm gay, and that I've had real struggles dealing with hiding that.
"I hid my emotions as a young ref and I hid my sexuality as well -- a good quality as a referee but a terrible quality as a human being. And that's led me to a whole course of behaviours."
Coote also addressed his use of cocaine.
"It's not something I was reliant on day by day, week by week, month by month," he said. "I've had long periods where I've not used it -- but it was one of the escape routes I had. Just getting away from the stresses, the relentlessness of the job. It fills me with a huge sense of shame to say that I took that route."
Coote remains under investigation by the Football Association (FA) for an alleged betting breach.
The incident related to a booking given to Leeds United's Ezgjan Alioski during a Championship match against West Bromwich Albion in October 2019. It was alleged he discussed issuing a yellow card with a friend before the match.
Coote has previously denied all allegations.
"I strongly refute these false and defamatory allegations," he said in November.
"Whatever issues I may have had in my personal life, they have never affected my decision-making on the field. I have always held the integrity of the game in the highest regard, refereeing matches impartially and to the best of my ability."
Coote first refereed a Premier League game in the 2017-18 season and was promoted to Select Group 1, the highest level of refereeing in the UK, for the following season.