In his 1905 paper on Brownian motion, Einstein derived the equation $$D=\frac{RT}{N}\frac{1}{6\pi kP}\tag{7}$$ where $T$ is temperature, $k$ is viscosity, $P$ is the radius of a spherical molecule (the Stokes radius) and $R$ and $N$ are constants.
A more familiar form used by Wikipedia is $$D=\frac{k_BT}{6\pi\eta r}$$ where $4k_B$ is Boltzmann's constant, $\eta$ is viscosity, and $r$ is the radius. The variant you have, $$\frac{D}{\mu}=V_t$$ arises from defining the thermal voltage as $$V_t\equiv\frac{k_BT}{q}$$ and writing the electrical mobility $\mu$ in terms of $q$ and $6\pi\eta r$.
Sutherland and Smoluchowski also did similar work to arrive at the equation, so they, too, deserve some credit.