Law enforcement sources tell us ... the 33-year-old actor was arrested in October for possessing 2.43 grams of cannabis at Arlanda Airport in Stockholm and was sentenced Wednesday.

We're told Bill was ordered to pay a fine of 40,000 Swedish krona -- approximately $3,825 USD and will not face jail time, probation or parole -- meaning it’ll all be behind him once he forks over the cash.

We’re told Skarsgård pled guilty to the crime and submitted paperwork to the court … and a judge sentenced BS based on that paperwork.

Bill -- who's starred in Stephen King's "It" and "Atomic Blonde" along with other well-known movies and TV shows -- is acting royalty in Sweden with his father Stellan and brothers Alexander, Gustaf, Valter, Ossian and Kolbjörn also members of the trade.