In this article, a Timoshenko system with local distributed Kelvin-Voigt damping is considered. More precisely, the authors consider the hyperbolic system \[ \begin{aligned} &\rho_1 w_{tt}-[\kappa(w_x+\phi)+D_1(w_{xt}+\phi_t)]_x=0,\\ &\rho_2\phi_{tt}-(\mu\phi_x+D_2\phi_{xt})_x+\kappa(w_x+\phi)+D_1(w_{xt}+\phi_t)=0, \end{aligned} \] for \((x,t)\in (0,L)\times(0,\infty)\), where \(\rho_1,\rho_2,\kappa\), and \(\mu\) are constants, \(D_1\) and \(D_2\) are functions of \(x\in[0,L]\), together with initial conditions \[ w(\cdot,0)=w_0, w_t(\cdot,0)=w_1, \phi(\cdot,0)=\phi_0, \phi_t(\cdot,0)=\phi_1 \text{ in }(0,L) \] and Dirichlet boundary conditions \[ w(0,\cdot)=w(L,\cdot)=\phi(0,\cdot)=\phi(L,\cdot)=0\text{ in }(0,\infty). \] To this initial-boundary value problem is associated an unbounded linear operator \(\mathcal{A}\) on a certain Hilbert space \(\mathcal{H}\) of quadruples of functions on \((0,L)\) which is motivated by the energy of the system \[ E(t)=\frac{1}{2}\int_0^L\kappa|w_x(x,t)+\phi(x,t)|^2+\mu|\phi_x(x,t)|^2+\rho_1|w_t(x,t)|^2+\rho_2|\phi_t(x,t)|^2\,dx, \] such that the initial-boundary value problem can be written as an evolution equation \(U_t=\mathcal{A}U, U(0)=(w_0,w_1,\phi_0,\phi_1)\) in the energy space \(\mathcal{H}\). Under mild assumptions on the coefficient functions \(C_1\) and \(C_2\) it is proved that \(\mathcal{A}\) generates a \(C_0\)-semigroup of contractions on \(\mathcal{H}\) and that \(i\mathbb{R}\) is contained in the resolvent set of \(\mathcal{A}\). Moreover, depending on certain regularity conditions of the coefficient functions \(C_1\) and \(C_2\), the authors prove polynomial/exponential stability, resp.\ analyticity, of the \(C_0\)-semigroup.