Nelson and his wife, Julie, have four children. When Nelson was seven, his father decided that each of his children would learn to play an instrument invented earlier than the 1800s. Nelson initially tried the violin but instead found his passion for the cello. He studied music and earned his degree at the University of Utah. Nelson credits his father with instilling his passion for music by his father displaying his own passion often. He openly credits God for his success but says that he does not want to push his beliefs on others or make others feel pressured by his music. As part of his faith, Nelson participated in a mission to South Korea.
As of 2006, Nelson was a real estate developer and described his music as an escape rather than a vocation. He never intended for music to become his primary income. Nelson signed with Stone Angel Music, an independent record label formed in 1999 by Paul Cardall, and released his first solo album, Sacred Cello, in 2006 earning him the Pearl Award for Best Instrumental Classical Album. The song reached the top 20 on the Billboard charts top 20 classical recordings. Nelson, and the rest of the Piano Guys, signed a contract with Sony Masterworks in 2012 that allowed them to retain artistic control of the group. He has also played with the China Philharmonic Orchestra. Nelson released two other solo albums: Tender Mercies in 2008, followed by Christmas Cello in 2010.