The insider said Martinez, 46, gave Berry, 45, a diamond and emerald ring when they got engaged during the holidays. 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."
UsMagazine.com quoted the unnamed source as saying Berry "had given up on being married but she trusts Olivier. He makes her feel safe. He's a keeper."
Ray Liotta sues skin care company over use of likeness
NBC reportedly holds celebs hostage to Jimmy Fallon's show