Vela.jl performs Bayesian pulsar timing and noise analysis. It supports narrowband and wideband TOAs along with most commonly used pulsar timing models. The code provides an independent, efficient, and parallelized implementation of the full nonlinear pulsar timing and noise model and includes a Python binding (pyvela). One-time operations such as data file input, clock corrections, and solar system ephemeris computations are performed by pyvela with the help of the PINT (ascl:1902.007) pulsar timing package.