We show that, under an irrotational condition, there exists an n-dimensional Hopf-Cole transformation between the n-dimensional Burgers system and an n-dimensional heat equation. Further, as application of the Hopf-Cole transformation, two kinds of physically interesting exact solutions for the n-dimensional Burgers equations are found. In the first kind of solutions, the velocity fields are topological solitons. In the second kind of solutions, velocity fields are all multiple fusion soliton solutions.