After graduating from high school in 1982, he first studied history and social sciences at the University of Bielefeld but later changed to law.

Torsten Albig was appointed candidate for Minister-President, representing his party, the SPD, in 2011 after a member's decision.

Together with Doris Ahnen, Martin Dulig, Heiko Maas and Manuela Schwesig, he co-chaired the SPD’s national convention in Leipzig in 2013.

[3] In the negotiations to form a Grand Coalition of Chancellor Angela Merkel's Christian Democrats (CDU together with the Bavarian CSU) and the SPD following the 2013 federal elections, Albig was part of the SPD delegation in the working group on transport, building and infrastructure, led by Peter Ramsauer and Florian Pronold.

In 2015, Albig – alongside First Mayor of Hamburg Olaf Scholz – negotiated a restructuring deal with the European Commission that allowed the German regional lender HSH Nordbank to offload 6.2 billion euros in troubled assets – mainly non-performing ship loans – onto its government majority owners and avoid being shut down, saving around 2,500 jobs.