Ringo marked the occasion on Instagram with a throwback photo of himself and his wife on their special day of 27 April, 1981.
“It was 40 years ago today The love of my life said yes yes yes. And I said it right back peace and love,” he wrote alongside the photograph.
In the photo, Starr and Bach are standing behind their wedding cake while the musician’s bandmates George Harrison and Paul McCartney pose either side of them with their own spouses, Olivia Harrison and Linda McCartney.
Meanwhile, Barbara’s young son Gianni from her first marriage to Count Augusto Gregorini was pictured standing in front of his mother.
John Lennon had been fatally shot less than five months earlier in December 1980. Linda McCartney died from breast cancer aged 56 in 1998, while George Harrison passed away from lung cancer at 58 in 2001.
George Harrison’s widow Olivia commented on the post: “What a day that was. I’m stunned by the passing years and each day of the love you have shared not only with each other but with the world around you.
“I love you both dearly. Happy Anniversary dear Rich and Barb.”
Starr – real name Richard Starkey – was first married to Maureen Cox from 1965 to 1975. They had three children, Zak, Jason and Lee.
US-born Bach is an actor, having appeared as Bond girl Anya Amasova in The Spy Who Loved Me opposite Roger Moore’s 007. In addition to Gianni, she had daughter Francesca with her first husband.