By studying the two-dimensional Su-Schrieffer-Heeger-Bose-Hubbard model, we show the existence of topological Higgs amplitude modes in the strongly interacting superfluid phase. Using the slave boson approach, we find that, in the large filling limit, the Higgs excitations and the Goldstone excitations above the ground state are well decoupled, and both of them exhibit nontrivial topology inherited from the underlying noninteracting bands. At finite fillings, they become coupled at high energies; nevertheless, the topology of these modes remains unchanged. Based on an effective action analysis, we further provide a universal physical picture for both their topological and phase-amplitude character at both infinite and finite fillings in a unified way. The discovery of topological Higgs amplitude modes in this paper opens the path to investigations in various systems, such as superconductors and quantum magnets.