Dylan Jason Syer, who began working for the Jumanji actor in 2015, is accused of making unauthorised purchases using Hart's credit cards.
He is alleged to have racked up the payments between October 2017 and February 2019.
The 29-year-old has been charged with grand larceny, criminal possession, identity theft and scheme to defraud.
If convicted, Mr Syer, from Long Island City in New York, faces up to 25 years in prison. He is due to return to court on 17 February.
Queens District Attorney Melinda Katz said the defendant legitimately gained access to the actor's credit cards, but then allegedly continued to use them to spend "astronomical sums of money".
Mr Syer is said to have bought items including Louis Vuitton bags and Patek Philippe watches. Ms Katz said he often posted pictures of the purchases on Instagram.