The main problem associated with using symmetric/ asymmetric keys is how to securely store and exchange the keys between the parties over open networks particularly in the open environment such as cloud computing. Public Key Infrastructure (PKI) have been providing a practical solution for session key exchange for loads of web services. The key limitation of PKI solution is not only the need for a trusted third partly (e.g. certificate authority) but also the absent link between data owner and the encryption keys. The latter is arguably more important where accessing data needs to be linked with identify of the owner. Currently available key exchange protocols depend on using trusted couriers or secure channels, which can be subject to man-in-the-middle attack and various other attacks. This paper proposes a new protocol for Key Exchange using Biometric Identity Based Encryption (KE-BIBE) that enables parties to securely exchange cryptographic keys even an adversary is monitoring the communication channel between the parties. The proposed protocol combines biometrics with IBE in order to provide a secure way to access symmetric keys based on the identity of the users in unsecure environment. In the KE-BIOBE protocol, the message is first encrypted by the data owner using a traditional symmetric key before migrating it to a cloud storage. The symmetric key is then encrypted using public biometrics of the users selected by data owner to decrypt the message based on Fuzzy Identity-Based Encryption. Only the selected users will be able to decrypt the message by providing a fresh sample of their biometric data. The paper argues that the proposed solution eliminates the needs for a key distribution centre in traditional cryptography. It will also give data owner the power of finegrained sharing of encrypted data by control who can access their data.