Key Agreement protocol (KAP) is one of the fundamental cryptographic primitives after encryption and digital signature which enables two or more entities arrive at a common key, which may be later used for any cryptographic purpose. In this paper we proposed an authenticated tripartite key agreement protocol. The decomposition search problem plays the role of one way function. The five dimensional Discrete Heisenberg group is chosen as the platform group which is non abelian. The KAP proposed in this paper is authenticated by digital signature. Thus, the proposed KAP satisfies all the necessary security attributes required.