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The Scots singer met Megumi Igarashi, 44, after supporting her campaign against Japanese authorities over her controversial artworks.
Igarashi, who is known as Rokudenashiko, is Japan’s self-proclaimed “vagina artist” and has created works such as a Lady Gaga model and a full-sized kayak modelled on her private parts.
The couple, who are expecting their first child together, had announced their engagement on a live streaming website and even invited Japanese police and prosecutors to the wedding as a thank you for bringing them together.
Scott, 57, whose hits include The Whole of the Moon, posted a photo of them smiling yesterday(with the message: “Just married.”
The newlyweds were sent dozens of messages of congratulations from well wishers.
Fellow Scots musician Edwyn Collins said: “Congratulations Mike!! Brilliant news -Edwyn.”
Helen Peel wrote: “Hurrah!!! The biggest smiles in the world... Congratulations to you both.”
Marion Black posted: “How wonderful, congratulations, you both look so happy. Sending love from Edinburgh!”
Scott met Igarashi for the first time in 2014, when a campaign to protest against her arrest by Tokyo police on obscenity charges caught his attention after gaining widespread international publicity.
Edinburgh-born Scott, who formed The Waterboys in the early 1980s, wrote a song supporting Miss Igarashi called Rok Rok Rokudenashiko and has expressed his admiration for her in the past.
He said: “Rokudenashiko is a brave artist, and her work, which celebrates the vagina in a playful way, isn’t obscene at all.
“She’s fighting a form of state censorship, and doing it on her own without any corporate or company backing. As a fellow artist, I support her. She’s also great fun and that inspired me to write a mischievous slice of psychedelic funk in her honour.”
The couple’s child is due in February and they hope to set up home in Dublin where Scott has lived for a number of years.