Andreas Voigt was born in Eisleben (GDR) on August 25, 1953, grew up in Dessau and completed his Abitur in Halle. He then studied physics in Krakow, Poland, before graduating with a degree in economics and economic history in Berlin. Voigt then turned to the film business and, from 1979, initially worked as a dramaturge for documentaries at the DEFA studio in Berlin before studying directing at the Potsdam-Babelsberg Academy of Film and Television.

From 1987 to 1990 he worked as a director at the DEFA Studio for Documentary Films. During this time, Voigt also began his series of Leipzig films, which have received international attention. It is comprised of five feature-length documentaries and tells the life stories and fates of people in Leipzig over a period of ten years. The series begins with "Alfred" (1986), Voigt's graduation film from film school. Other parts focus on events in the period of upheaval during the fall of the GDR and the beginnings of a unified Germany. Among them are "Leipzig im Herbst" ("Leipzig in the Fall") and "Letztes Jahr – Titanic", for which Voigt was awarded the Adolf Grimme Prize in 1991.

Since the closure of the DEFA studio in 1991, Voigt has been active internationally as a freelance director, writer and producer. He also conducts seminars on documentary work and takes on teaching assignments in Hamburg, Berlin, Paderborn, India, Syria and Singapore.

In addition to numerous TV productions and image films for the German government, among others, Voigt realized another project for the big screen in 2004 with "Invisible - Illegal in Europa" ("Invisible - Illegal in Europe"). The award-winning documentary tells the story of five refugees of different origins who are staying illegally in Europe.

In the following years, Voigt worked primarily for television. As a German-French production, he made "Les Nomades du Cercle Polaire" (2007), in which Voigt accompanies two nomadic families traveling with their five thousand reindeer across the Ural Mountains from Europe to Asia. In 2009 he was involved in the mammoth project "24h Berlin", and for the Grimme Award-winning project "20 x Brandenburg" he made "Der Landpfarrer" (2010), about a pastor in the Uckermarck region.   

Between 2010 and 2019, he made three approximately 50-minute documentaries for public braodcaster SWR/Arte: "Im Kaukasus - Samuchas letzter Sommer" ("Samucha: Last Journey of a Sheperd", 2010), about a Georgian high valley herdsman reminiscent of American cowboys, "Die Mahouts von Kerala" (2014), about two elephant handlers in southern India, and "Mit Kamelhirten durch die West Sahra" (2019).    

For the big screen, he realized "Alles andere zeigt die Zeit" (2015), which concluded the above-mentioned Leipzig series begun in 1987. For this film, Voigt was awarded the Bavarian Film Prize for Best Documentary. Also in 2015, he was among the directors of the documentary episodic film "Als wir die Zukunft waren...", in which seven filmmakers from the former GDR review their childhood and youth memories. In 2019, Voigt was involved in the project "24H of Europe."   

Voigt's next feature documentary premiered at the DOK Leipzig festival in 2020: "Grenzland", a sequel to his 1993 documentary "Grenzland - Eine Reise", which was theatrically released in summer 2021.