The coronation ceremony was witnessed by royalty and European heads of state.
43-year-old Guillaume is Luxembourg's seventh grand duke since 1890 when the modern monarchy was established.
Grand Duke Henri, 70 years old, has sat on the throne for almost 25 years and has mainly had representative duties as the country's monarch.
The Swedish royal family has distant family ties to the monarchy in Luxembourg. The now incoming Guillaume's grandmother was the daughter of King Leopold III of Belgium and Princess Astrid of Sweden, and is thus a distant relative of King Carl XVI Gustaf.
Corrected: In an earlier version, an incorrect description of the family ties to the Swedish royal family occurred.
What do you think?