APeter Baumann was born in Berlin, Germany, in 1953, his father a composer, his mother an actress. When he was eight, the Berlin Wall was built, and Baumann entered the American/German Community School in Berlin, where he learned English and was first exposed to American culture. At age 14, Peter joined a cover band and performed at G.I. clubs. Then, in 1971, at age 18, he met Christopher Franke, and ended up joining Tangerine Dream in replacement of their former organist Steve Schroyder. Two years later, Tangerine Dream signed with Virgin Records and their first album on the label, Phaedra, became a Top 10 seller on the Melody Maker charts. As a result of this and other recording successes, Tangerine Dream toured the world for eight years. They also made successful forays into film scoring. Baumann had temporarily left Tangerine Dream twice, first in 1973 (returning in time for Franke & Froese to shelf their current work on Green Desert and the three to start anew on what was to become Phaedra), and again in 1975, leaving Michael Hoenig as a temporary substitute for an Australian tour. His departure in 1977, shortly after the completion of the band's first U.S. tour, was final and led to a brief solo career.

From 1984 to 1996 he ran his label Private Music, specializing in instrumental music in a style popularly referred to as New Age. Artists signed to the label included Yanni, Patrick O'Hearn, Jerry Goodman, Suzanne Ciani, and former bandmates Tangerine Dream. In 1996, the label was sold to Windham Hill Records' parent company, BMG, who continue to distribute some of the back catalogue of its more successful artists. Baumann has since kept a low profile from the music business, devoting his time to studying Eastern and Western spiritual traditions, religions and philosophies. He has since founded the Baumann Institute and developed a philosophical theory focused on human suffering and liberation called Natural Enlightenment. Since 2009 he is head of the Baumann Institute, dedicated to exploring the nature of awareness and its relationship to human health and well-being.