Peter Tschentscher was born on 20 January 1966 in Bremen. Beginning in 1987, after secondary school and civilian service, he studied medicine with postgraduate studies in molecular biology in Hamburg, which he completed with a Doctor of Medicine degree in 1995. This was followed by a Habilitation in 2008. Until 2011, he was a senior physician at the University Medical Center Hamburg-Eppendorf.
Peter Tschentscher joined the SPD as a student. From 2008 to 2011, he was Deputy Chair and Financial Policy Spokesman of the SPD faction in the Hamburg Parliament. In 2011, he was named Minister of Finance in the Hamburg Senate.
On 28 March 2018, the Hamburg Parliament elected Peter Tschentscher as the First Mayor of the Free and Hanseatic City of Hamburg.