In this paper, we present the Legendre wavelets based method for the solution of homogeneous and nonhomogeneous advection problems. The properties of Legendre wavelets are used to reduce the problem to the solution of system of algebraic equations. The function approximation has been chosen in such a way so as to calculate the connection coefficients in an easy manner. Also the convergence analysis and error estimation for the proposed function approximation through the truncated series have been discussed and approved with the exact solution. Illustrative examples are discussed to demonstrate the validity and applicability of the technique.