After cancelling an apprenticeship in Magdeburg, a chance acquaintance with Friedrich Nicolai led him to become a bookseller in the Halle Orphanage bookstore.

Duke Karl Wilhelm Ferdinand wanted to establish a Book Fair and make Braunschweig the center of the German bookselling trade.

At the Duke's request, Vieweg moved there in 1799 and was presented with some land and a dilapidated theater where he could set up his operations.

When sovereignty was restored in 1815, he became involved in politics and public works administration, serving for some time as a city councillor.

From 1826 to 1828, he produced the "Mitternachtblatt für gebildete Stände" (Evening Journal for Educated Readers) in cooperation with Adolf Müllner but, due to some disagreements, it was sold to Niedmann’s Verlag in Wolfenbüttel.