Moser was born on June 14, 1979, in Munich, Germany. His father was a German violinist, his mother a Canadian soprano, and he has retained dual German and Canadian citizenship. He lived in Germany, however, until moving to New York in 2012. Moser took up the violin at age five and then switched to the cello at eight. His first teacher was his father, but "[e]ventually, there was a little bit of a clash," he told the Dallas Observer. "I think we decided at some point that for the sake of peace at home, it would be better for me to move on." Studying with David Geringas, a student of Mstislav Rostropovich who worked in Germany during the latter part of his career, Moser developed an independent voice.
His first breakthrough was a silver medal showing at the 2002 Tchaikovsky Competition, performing Tchaikovsky's Variations on a Rococo Theme, Op. 33. He has since become identified with that cello showpiece, performing it dozens of times. Moser signed with the Haenssler label and recorded sonatas by Shostakovich, Mieczyslaw Weinberg, and Boris Tchaikovsky for his 2006 debut. That was followed by an album covering Saint-Saëns' complete works for cello and orchestra and by an acclaimed three-volume Brahms and His Contemporaries series; Moser earned the Brahms Prize in 2014. Several more major concerto releases propelled Moser to top-level concert slots under such conductors as Riccardo Muti, Mariss Jansons, and Gustavo Dudamel, among many others.
In 2015, Moser signed with the audiophile label PentaTone and announced plans for a new group of major repertory recordings. That began with a pairing of concertos by Lalo and Dvorák and continued in 2017 with a disc featuring the Elgar Cello Concerto in E minor, Op. 85, and the Tchaikovsky Rococo Variations. Termed a "rock star cellist" by the Observer, Moser is an informal and fashionable dresser who listens mostly to non-classical music on recordings (he prefers to experience classical music in concert). He has expressed a serious commitment to teaching aspiring musicians from kindergarten level on up. Moser is also an enthusiastic chamber musician who has performed with Joshua Bell, Emanuel Ax, and Jonathan Biss, among others. A top-notch cyclist, he has ridden across the Alps but has curtailed his long-distance cycling activity in order to protect his hands. ~ James Manheim, Rovi