The Ultraviolet star revealed her plans to wed Anderson in a small service earlier this month.
The couple exchanged matching 18 karat gold wedding rings designed by Neil Lane, People reports.
Lane said: "They're a super duper couple. They clearly adore each other."
The ceremony was reportedly preceded by a cocktail reception featuring Spanish musicians and followed by performances from traditional Cuban artists.
Last week, Jovovich revealed that she had accidentally given Anderson a black eye during the filming of the first Resident Evil movie.