The bride, 29, wore a beautiful Vera Wang gown next to a bejewelled headband and a bouquet of purple lilies.
The groom wore a white Tom Ford tuxedo with bow tie.
Among the wedding guests were the couple’s families and close friends and also celebrities such as Bono, U2 frontman, and Queen Latifah.
Alicia and Swizz Beats started dating 2008 and later this year will be parents. The singer is due to give birth in November.
The two arrived in Corsica several days earlier the wedding and enjoyed sunbathing next to several celebrity friends.