The couple, who have two children – three-year-old twins Max and Emme – reportedly released a joint statement to People.com.
According to the US celebrity news website, the 41-year-old singer-actress and Anthony released a statement, saying: “We have decided to end our marriage.
“This was a very difficult decision. We have come to an amicable conclusion on all matters.”
This is the third marriage for the American Idol judge, who was previously married to former back-up dancer Cris Judd, who she divorced in 2003 after two years of marriage, and Cuban waiter Ojani Noa, from whom she split in 1998 after a whirlwind romance that lasted just 10 months.
She married Anthony in a surprise ceremony in June 2004.
The 42-year-old Latin singer-songwriter has also been married before – to Puerto Rican actress Dayanara Torres, with whom he has two children.
The Jenny From The Block singer has also had high-profile romances in the past with rapper P Diddy and Oscar-winning actor Ben Affleck, to whom she was engaged.