Sheremet and Rimes were married for seven years, but separated in 2009 after the recording star had an affair with actor Eddie Cibrian, who she has since married.
Sheremet and Silver got engaged last November.
People.com said Tuesday Sheremet posted a video of himself and his new bride kissing outside of an unidentified city clerk's office.
A message accompanying the clip reads, "Happy happy day."
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