IP-based Wireless Sensor Networks (IP-based WSNs) combine IPv6 technology with WSNs to create a global sensor network infrastructure. However, wireless radio access and Internet connectivity make end-to-end security urgently needed by security critical WSN applications. Transport Layer Security (TLS) is considered as a suitable solution to ensure such security. However, the certificate-based mechanism used by the TLS handshake protocol has a complex certificate management overhead and long handshake latency. Identity Based Cryptography (IBC) provides a viable alternative to the use of certificates. In this paper, we propose two improved TLS handshake protocols for IP-based WSNs using IBC. The first uses IBC and Elliptic curve Diffie Hellman (ECDH) protocol for key exchange and agreement while the second uses a variant of IBC based on Elliptic Curve Cryptography (ECC) and bilinear pairing. Security analysis shows that improved TLS ensures security requirements for IP-based WSN. AVISPA tool is used to validate the proposed improvements. In addition, performance analysis shows that TLS handshake protocol using IBC gives better performance in terms of latency and energy consumption.