Levit began playing piano at age three, and as a child he had his first successes on the concert stage in his hometown of Nizhny Novgorod. His family moved to Hanover in 1995. From 1999-2000 he studied at the Mozarteum in Salzburg with Hans Leygraf and from 2000-2010 at the Hochschule für Musik, Theater und Medien Hannover with Karl-Heinz Kämmerling, Matti Raekallio and Bernd Goetzke.
Levit has appeared in major concert halls and music festivals around the world. During his studies he won several international awards, including second prize at the International Maria Callas Grand Prix, Athens (2004), first prize at the International Piano Academy Competition in Hamamatsu (2004), the silver medal and three other awards at the Arthur Rubinstein International Piano Master Competition in Tel Aviv (2005), and the Luitpold Prize for young artists at the Festival Kissinger Sommer in Bad Kissingen (2009). In October 2011 he appeared in a 45-minute documentary aired on 3sat about his love for the music of Franz Liszt. He was a BBC Radio 3 New Generation Artist from 2011 to 2013.
In 2013 Levit released his debut album, a two-disc set of Ludwig van Beethoven's late piano sonatas (Nos. 28 to 32), on Sony Classical Records. His second Sony album, a recording of Johann Sebastian Bach's six keyboard partitas, was named Gramophone Magazine's recording of the month for October 2014. His third Sony album, a 3-CD set of Bach's Goldberg Variations, Beethoven's Diabelli Variations, and The People United Will Never Be Defeated! of Frederic Rzewski, was released in October 2015.