The custom-made piece of jewellery features the names of babies Moroccan and Monroe.
It is 14 carat white and rose gold and contains more than four carats of white diamonds and pink sapphires.
Cannon gave the necklace to Carey to mark the arrival of the twins and Mother’s Day, which this year was celebrated on May 8 in America.
It was designed by Jason Arasheban of jeweller Jason of Beverly Hills.
He said: “Nick was really excited about the babies’ names and wanted to do a piece with them for Mariah’s first Mother’s Day.”