The Miami Herald said Martinez discussed his plans to wed while he was in the Florida city to promote his new restaurant, Villa Azur, which opened Saturday.
Asked about the engagement buzz, the Herald said Martinez replied, "Yes, of course, it's true."
He shot down another rumor, however.
"There is a jeweler taking credit for doing the ring and it's a lie! They have nothing to do with this," he said, adding Berry's emerald and gold sparkler was actually designed by Robert Mazlo, a jeweler in Paris.
There was no word on whether the couple have set a wedding date after getting engaged over the Christmas holiday. They began dating in the fall of 2010.
Berry, an Oscar winner for her work in the film "Monster's Ball," has a 3-year-old daughter with her ex-boyfriend Gabriel Aubry.
Martinez's film credits include "Before Night Falls," "Unfaithful," "S.W.A.T." and "Taking Lives."