In this paper we present a combinatorial proof of Selberg's integral formula. We prove a theorem about the number of topological orderings of a certain related directed graph bijectively. Selberg's integral formula then follows by induction. This solves a problem posed by R. Stanley in 2009. Our proof is based on Anderson's analytic proof of the formula. As part of the proof we show a further generalisation of the generalised Vandermonde determinant.