The major arboviruses mainly belong to the Bunyaviridae, Togaviridae, and Flaviviridae families, among which the chikungunya virus and dengue virus have emerged as global public health problems. The main objective of this study was to develop specific, sensitive, and cost-effective molecular multiplex RT-PCR and RT-qPCR assays for the rapid and simultaneous detection of CHIKV and the four serotypes of DENV for arbovirus surveillance. Specific primers for all viruses were designed, and one-step multiplex RT-PCR (mRT-PCR) and RT-qPCR (mRT-qPCR) were developed using reference strains of the CHIKV and DENV serotypes. The specificity of the test for all the viruses was confirmed through sequencing. The standard curves showed a high correlation coefficient, R2 = 0.99, for DENV-2 and DENV-3; R2 = 0.98, for DENV-4; and CHIKV; R2 = 0.93, for DENV-1. The limits of detection were calculated to be 4.1 × 10−1 copies/reaction for DENV-1, DENV-3, and CHIKV and 4.1 × 101 for DENV-2 and DENV-4. The specificity and sensitivity of the newly developed mRT-PCR and mRT-qPCR were validated using positive serum samples collected from India and Burkina Faso. The sensitivity of mRT-PCR and mRT-qPCR are 91%, and 100%, respectively. The specificity of both assays was 100%. mRT-PCR and mRT-qPCR assays are low-cost, and a combination of both will be a useful tool for arbovirus surveillance.