The Edinburgh-born author announced the news on Instagram on Wednesday.
Alongside a picture of the couple sat on a bench in their wedding attire with Currie’s bouquet to one side, the 63-year-old wrote: “Knot tied. All good in the world. See you later, alligators.”
Currie also shared two of images of the occasion to her own Instagram page, simply captioned: “Today I married the love of my life.”
Welsh, who has now married for a third time, revealed he had proposed to Currie in a post on his Instagram earlier this year.
The author captioned an image of Currie smiling and showing her ring to the camera: “My god. She said yes. Pissing wet day in Scotland but she said yes. So f*** everything else. Never been so happy in my life.”
A few months back, it was reported that a new documentary will shine light on Welsh’s childhood in Edinburgh and his rise to literary stardom.
Choose Irvine Welsh will take a look at the Hibs-daft writer's childhood in Leith, his teenage years in the 1970s, and his rise to literary stardom.
Produced and narrated by Welsh himself, the documentary features interviews with Trainspotting director Danny Boyle, the film's stars Robert Carlyle and Ewan McGregor, and Oasis legend Noel Gallagher, among others.
It will see them detailing various encounters with Welsh over the years.
Born in Leith in 1957, Welsh moved to Muirhouse at the age of four where the wave of crime and drug abuse that consumed the area shaped much of his later work.
He left Ainslie Park High School at 16 and departed for London’s flourishing punk scene in 1978.
Welsh returned to the Capital in the early 80s, taking a job as a training officer in the housing department.
He shot to stardom when debut novel Trainspotting was published in 1993 – less than three years before the film adaptation was released.
Its sequel, T2 Trainspotting, was released more than two decades later in 2017.
Welsh has written several other novels including Filth and Skagboys.
As yet, no release date has been given for Choose Irvine Welsh.