The couple tied the knot on the French island of Corsica last weekend and his nine-year-old child Prince Nasir Dean was given the responsibility of handing over the rings to his dad and new stepmother.
An eye witness to the nuptials told Life & style magazine: "The whole ceremony was magical, like something out of a dream."
Swizz - who has two other children, son Kasseem Dean, Jr. and daughter Nicole, from previous relationships - and his pregnant bride Alicia's vows were witnessed by Queen Latifah, U2 frontman Bono, Tommy Hilfiger and Christian Louboutin, who designed the sandals worn by the 'Empire State of Mind' singer on her big day.
Since tying the knot Swizz, 31, has admitted he has never been happier since he made the 29-year-old musician his wife.
He said: "I love everything about her."
This is the first marriage for Alicia, while Swizz has been wed once before.
The couple's baby is due in November.