"This was a very difficult decision," the pair said in a statement. "We have come to an amicable conclusion."
The couple, who have three-year-old twin children, said "we appreciate the respect of our privacy".
Lopez, 41, and Anthony, 42, toured together and starred together in the 2006 film El Cantante.
The film was a biopic of Puerto Rican singer Hector Lavoe.
The divorce will be Lopez's third and Anthony's second.
In January Lopez became a judge on American Idol. She and Anthony in April announced plans for a television show called Q'Viva! The Chosen with American Idol creator Simon Fuller.
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