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The couple tied the knot in a private ceremony in Texas before close friends and family, including their two young kids, with Alves taking the groom's last name to become Camila McConaughey, the actor's rep told the magazine.
McConaughey, 42, and Alves, 30, were engaged in December but kept the date of the wedding on his estate secret.
Named the "sexiest man alive" in 2005 by People, McConaughey starred in "Lincoln Lawyer" (2011), with Penelope Cruz in "Sahara" (2005), in "How to Lose a Guy in 10 Days" (2003) with Kate Hudson, and with Jennifer Lopez in "The Wedding Planner" (2001).
McConaughey showed up at Cannes in May to promote his latest films "Paperboy" and "Mud."