The trust, authenticity and integrity of Internet-of-Things (IoT) systems are heavily reliant on Physical Unclonable Functions (PUFs) and True random number generators (TRNGs). The PUF and TRNG produce device intrinsic digital signatures and random binary sequences, which are used for cryptographic key generation, key agreement/exchange, device authentication, cloning prevention etc. This article reports an efficient Field Programmable Gate Array (FPGA)-based realization of elliptic curve Menezes-Qu-Vanstone (ECMQV)-authenticated key agreement protocol using PUF and TRNG with very competitive area-throughput trade-offs. The key agreement protocols, which establish a shared secret key between two IoT devices, make use of PUF and TRNG primitives for the long-and short-term secret keys generation while the elliptic curve is employed for public key generated from the corresponding secret key. The performance of the protocol is investigated on FPGAs. The authors' implementation of the ECMQV protocol takes 1.802 ms using 18852 slices on Artix-7 FPGA.