The doors were shut for the service, which is thought to have included some guitar music as musicians were spotted at the venue earlier in the day.
It is understood the couple chose the remote Scottish location as they have enjoyed happy holidays in the area.
He said his confession would help them to move on, and he wanted to be with his wife "for life". He said: "I know that sounds really stupid but on our wedding day, for me the ring is really important and I want to be true to my word." "The wedding for me was a new slate and a new start.
,but went on to be one of the band's most popular members.
Owen, 38, who has often been seen as a "squeaky clean" member of the reunited group, said earlier this week that he was "deeply sorry" for the "pain" he had caused to his wife and friends through his flings with as many as 10 women.
But he insisted he had been faithful since marrying her in November.
Shortly before Derek's move to Seattle, Mark and Addison were caught having sex in Derek's bedroom.
Ferguson kept her groom waiting, as is tradition, arriving at 4.55pm for the service.
Wearing a white fitted wedding dress with V-neck and a lace antique style veil, she was accompanied by two bridesmaids, also in white.
They then made their way through the church grounds to a rear exit, and it is understood they made their way on to nearby Cawdor Castle, where the wedding reception was being held.
The couple have two children, toddler Elwood and Willow Rose, who was born last November.