The 73-year-old singer tied the knot at the registry office of her wealthy Zurich-area community with Bach, a 57-year-old music executive, said Markus Ernst, the mayor of Kuesnacht, where Turner owns a lakeside chateau.
Ernst told The Associated Press that the couple, whose relationship began in the 1980s, had a typical civil ceremony several weeks ago at the registry office, sometime between late June and early July.
The mayor described it as routine, other than some noise from construction outside the town building.
"It was really completely normal, just like anybody else," he said. "This Sunday is the wedding celebration. It's a private celebration they are having, and everybody says it's at their home, and most probably that's the case."
What's it like having the "Queen of Rock" as a neighbor?
"Of course she's most probably the best known inhabitant of our community," said Ernst, who described the eight-time Grammy-winner as someone who enjoys Switzerland's famous discretion toward celebrities.
"She's really a normal inhabitant," he said. "You can meet her in a restaurant. You can meet her like anyone else."
Her first marriage was to her former musical partner, Ike Turner, whom she divorced and famously wrote about in her autobiography-turned-movie. Turner, who was born Anna Mae Bullock in Nutbush, Tennessee, became a Swiss citizen earlier this year, after living in her Chateau Algonquin along Lake Zurich for nearly two decades.
After leaving her abusive first husband, Turner became best known as a hard-touring solo performer for her album "Private Dancer" and hits like "What's Love Got To Do With It?"
Swiss newspaper Schweiz am Sonntag reported that pop stars David Bowie and Sade and talk show impresario Oprah Winfrey were among the more than 120 guests who were invited for the private ceremony at the chateau and would be taking up weekend residence at some of Zurich's finest luxury hotels.
A small concert stage was being set up in the garden, the Sunday newspaper said, and Turner and Bach wrote neighbors to apologize in advance for any noisy disturbances.