Miami Beach Police said the Irish fighter slapped the victim’s phone out of his hands and “stomped on it several times” after the man attempted to take a picture of the MMA star.
The report added: “The defendant then picked up the victim’s phone and walked away with it.”
The alleged victim, a 22-year-old from Slough, said the phone was worth around 1,000 US dollars (£755).
McGregor has been charged with “strong-arm robbery and criminal mischief” after the incident outside the Fontainebleau Hotel on March 11.
It comes after the 30-year-old fighter had a brush with the law in the US over a violent incident at a UFC event.
Several people were hurt when he hurled a trolley at a bus, smashing a window, as it left the Barclays Centre in Brooklyn in April 2018.
Fighters Michael Chiesa and Ray Borg were injured by shattered glass and unable to compete.
McGregor later pleaded guilty to disorderly conduct and avoided going to jail after striking a deal with prosecutors.
He was given a community order and sent on an anger management programme.
UFC president Dana White described the fighter’s actions as “the most disgusting thing that has happened in the history of the company”.
A former UFC featherweight and lightweight champion, McGregor has become one of the sport’s biggest stars and a global celebrity.
According to Forbes he is worth around 100 million US dollars (£75 million), while his social media accounts show a life lived in luxury on private jets and behind the wheels of high-performance cars.
In a statement on Instagram accompanying a picture of him leaving jail, McGregor wrote: “Patience in this world is a virtue I continue to work on.
“I love my fans dearly. Thank you all.”