Reichelt studied economics, sociology and philosophy in Frankfurt where Theodor W. Adorno supervised his diploma in 1968.
In 1971 he became professor of sociology at the Johann Wolfgang Goethe University Frankfurt am Main.
On the initiative of Alfred Sohn-Rethel, Reichelt accepted the Professorship for social theory at the department of Sociology at the University of Bremen in 1978.
[1][2] Already during his time as a university student he began a long-term cooperation with Hans-Georg Backhaus.
Reichelt also oversaw an edition of Hegel's Philosophy of Right in the Ullstein Verlag.