The couple tied the knot on Tuesday in the Dominican Republic, in a ceremony which is said to have taken place in front of close friends and family.
News of the wedding comes after Marc posted a photo of the couple walking together on Instagram back in September, which he captioned: "Have a surprise coming for you! Get ready!"
Marc and model Shannon have been dating on and off since 2012, while he also dated Topshop heiress Chloe Green for a year between 2013 and 2014.
However, his most high-profile relationship has been with ex-wife Jennifer Lopez, with whom he has six-year-old twins Max and Emme. His and Jennifer's divorce was only finalised in June, although they split in 2011.
The singer also has four other children from previous relationships, while Shannon has a seven-year-old son.
Jennifer recently said that she is enjoying the single life, saying that "I gotta be happy and whole on my own".
More stars who married in 2014
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