Published Friday, 08 June 2012
Rumours about of the secret nuptials spread this week after Alves opted to deliver a speech at the Step Up Women's Network gala in Beverly Hills on Saturday via video rather than actually attend the luncheon.
And now insiders tell E! News she chose to skip the event and get married instead.
Reports suggest McConaughey and Alves have invited just two dozen close friends and family members to the ceremony.
A representative for the couple could not be reached for comment.
McConaughey and his 30-year-old bride-to-be, a model and handbag designer, became engaged on Christmas Day.
The couple began dating in 2006 and have two children, two-year-old daughter Vida and son Levi, who turns four next month.