Born in Heilbronn, Wittmann studied musicology from 1975 to 1980 (with Hans Heinrich Eggebrecht), philosophy and history at the Albert-Ludwigs-Universität in Freiburg im Breisgau.
From 1980 to 1983 and 1987 he was a scholarship holder of the German Historical Institute in Rome.
Since 1991 Wittmann has been a research assistant at the Musicological Institute of the Free University of Berlin.
As scientific advisor to the Berolina-Ensemble he has initiated the revival of forgotten composers such as Iwan Müller, Ernst Rudorff, Waldemar von Baußnern, Conrad Ansorge; in the same capacity Wittmann has initiated the rediscovery of operas by Saverio Mercadante, Michele Carafa and Francesco Morlacchi for the Rossini-Festival in Bad Wildbad.
His editions of Otto Nicolai's previously lost operas Il templario and Die Heimkehr des Verbannten have led to a reassessment of this composer.