The 43-year-old singer has embarked on a romance with Venezuelan model Shannon De Lima - who has a four-year-old son from a previous relationship - following the breakdown of his marriage to Jennifer Lopez, who he split from in July after seven years of marriage.
He posted a message on twitter in Spanish which translated as: "To Shannon, my statue of liberty. Kisses baby!"
On his Facebook page, Marc posted a picture of himself embracing Shannon, captioning it "Gracias", the Spanish word for thank you.
Marc`s adopted son Chase Muniz - from his relationship with Debbie Rosado - also used twitter to praise his dad`s new romance.
He wrote: "To all my followers and everybody on twitter follow 2012 best couple and for many more years to come @MarcAnthony and @Shadelima !!!!!
"Life is beautiful nothing like being surrounded by the people you love @MarcAnthony @Shadelima !!!!!! #family (sic)"
Since Marc and Jennifer - who have three-year-old twins Max and Emme together - separated, the `American Idol` judge has been romantically linked with actor Bradley Cooper and is now dating 24-year-old dancer Casper Smart.