"We have decided to end our marriage. This was a very difficult decision. We have come to amicable conclusion on all matters," they said in a statement to People magazine.
"It is a painful time for all involved, and we appreciate the respect of our privacy at this time."
The singer-actors are parents to three-year-old twins Max and Emme.
Anthony, 42, and Lopez, 40, dated briefly in the 1990s before marrying in 2004.
Lopez's star has been on the rise thanks to her visibility as a judge on America's most popular television show and as a ubiquitious pitchwoman for beauty products.
They renewed their vows last year, after rumors that there were problems in the marriage, that they two had stopped appearing together in public and that Lopez had stopped wearing her wedding ring.
And Anthony became a staple on "American Idol," when Lopez became a judge. He was in the audience at nearly every show, was a mentor one week and even did a solo singing spot on the season finale, with Lopez onstage dancing along.