The couple, who have two children Levi, 3 month, and daughter Vida, 2, tied the knot in a ceremony attended by close friends and family on June 9, reported People Magazine.
A representative for 42-year-old actor has confirmed about the nuptials and said Alves is all set to take the groom's last name.
Wedding guests included actor Woody Harrelson and filmmaker Richard Linklater, who camped out the night before in the back garden of McConaughey's Austin compound. They stayed in two-person luxury tents with air-conditioners.
McConaughey, who met the model turned designer in a Los Angeles bar in 2006 and began dating soon afterward, proposed to her on Christmas Day.