The intimate ceremony took place in front of close friends and family at midday on Saturday.
The museum is near the site of California's first mission, founded by Spanish Franciscan missionary Father Junipero Serra in 1769.
She wrote on her Facebook page: "Today has been a very special day for which I waited a long time. I married the love of my life, Jacob. Thanks so much for your prayers and support."
The wedding comes four months after Jacob proposed to Rebecca at her family farm in Franklin, Tennessee, on Christmas Day.
Jacob is originally from Colorado and previously spent two years as a missionary in South Africa, before studying communications at college and entering the music industry.
The couple met through mutual friends in Los Angeles.
Rebecca has earned the respect of girls and women the world over with her message of purity before marriage and her signature song, "Wait For Me", released back in 2000, was a declaration of her commitment to live out her message.
This month also saw the release of her new studio album "I Will Praise You".
Never one to rest on her laurels, Rebecca is putting the finishing touches to her ninth book, "What Is He Thinking", due out in September.