We investigate the electronic transport properties of silicon nanotubes attached to metallic electrodes from first principles, using density functional theory and the non-equilibrium Green's function method. The influence of the surface termination is studied as well as the dependence of the transport characteristics on the chirality, diameter, and length. Strong electronic coupling between nanotubes and electrodes is found to be a general feature that results in low contact resistance. The conductance in the tunneling regime is discussed in terms of the complex band structure. Silicon nanotube field effect transistors are simulated by applying a uniform potential gate. Our results demonstrate very high values of transconductance, outperforming the best commercial silicon field effect transistors, combined with low values of sub-threshold swing.