The 'Empire State of Mind' singer – who is five months pregnant with the couple's first child – tied the knot with the music producer on the French island of Corsica.
Alicia, 29, wore an ivory silk, Grecian-inspired gown designed by Vera Wang with crystal-encrusted flat sandals, an elegant headband and a bouquet of purple calla lilies.
The groom – real name Kaseem Dean - wore a Tom Ford tuxedo with an ivory jacket.
Celebrity guests included U2 rocker Bono and Queen Latifah, while the ceremony was conducted by the couple's close friend Deepak Chopra – who was a close friend of Michael Jackson's before his death.
This is the first marriage for Alicia, while 31-year-old Swizz has been wed before and has two sons.
Swizz took to twitter after the ceremony to express his joy.
He tweeted: "Wowwwwwwwwww."
And later wrote: "It's a brand new day :) I feel like Nas and Diddy song :) love y'all and blessing! (sic)"
Alicia announced her pregnancy and engagement in May, with a friend saying at the time: "She is thrilled. She is with the man who has inspired so much of her music."