The 56-year-old former glamour model and pop star married her Norwegian tour manager at King's Oak Hotel in Essex, with former UK and Norway winners of the song contest performing at the party.
Both brides wore traditional white gowns and veils and exchanged diamond wedding rings.
Fox's dress was sleeveless with a jewel-encrusted bodice. It was knee-length at the front to show off her legs, with a long jewel-embroidered train at the back.
Olsen's gown was short-sleeved and floor-length.
The eight bridesmaids all wore pale pink and the bouquets and floral decorations were made from pale pink and white roses.
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The three tier wedding cake was decorated with silver topper reading, "Mrs and Mrs Olsen-Fox".
Both brides were joined by their mothers Carole Fox and Jorunn Olsen, as well as Olsen's sons Adam and Noah.
Katharina Leskanich, of UK Eurovision winners Katrina and the Waves, performed at the ceremony, along with Norwegian Eurovision Song Contest champions Elisabeth Andreassen and Hanne Krogh of Bobbysocks.
Norwegian singer Lisa Stokke also sang at the wedding.
Fox was in a relationship with her manager Myra Stratton for 16 years before she died in 2015 aged 60.
She and Olsen became engaged in February 2020.
Fox recently confirmed she is due to have surgery to remove a lump from her vocal chords.
The 80s pop star revealed she had undergone a cancer scare after doctors found the 10mm lump.
Fox told GMB: “I've got an operation on my throat coming up very very soon and I'm getting a lot of messages off people who are very worried because they're not sure whether it's sinister or not.
“So I'd just like to say to my fans out there, I'm having it done.
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“As soon as I'm married I'll be getting it taken out and I'm sure everything is going to be fine.”