The 33-year-old star, who played Tori Spelling's love interest David Silver on the hit series, was previously engaged to costar Vanessa Marcil.
Green and Marcil have one son together, Kassius, 4.
Fox, 20 has appeared on the sitcoms Hope & Faith and Two and a Half Men and appears in the upcoming Transformers film.
Green tells Us Weekly magazine that no official wedding date has been set and that the couple may decide to elope.
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