Couric tweeted a picture with the message: "So excited to make my debut as Mrs. John Molner!"
Molner, 51, is a partner at investment firm Brown Brothers Harriman overseeing mergers and acquisitions for the firm's corporate clients.
The couple got engaged last September after dating for about two years.
Couric's first husband, Jay Monahan, passed away in 1998 from colon cancer.
Couric, 57, has two grown daughters. Molner has a son and a daughter.
The Associated Press contributed to this report.